Chapter 8: Hypothesis Testing

Question 1

Define hypothesis:

A: A concrete and proven statement that accurately reflects the true value of a population parameter, providing a definitive answer to a research question.

B: A prediction. For example, we don’t know the true value of the population mean, so we replace its unknown value with a hypothesis. We then use the sample mean (an estimate) to infer the population mean (a parameter).

C: A random guess or assumption made without any basis or prior information, often used in research to see if the data supports this arbitrary idea.

Answer 1

B: A prediction. For example, we don’t know the true value of the population mean, so we replace its unknown value with a hypothesis. We then use the sample mean (an estimate) to infer the population mean (a parameter).

To test a hypothesis we can:
> Look at the p-value and confidence interval in order to refute/reject or accept/support a hypothesis

Question 2

Define “specify a hypothesis:”

A: Creating a statement that is deliberately vague and ambiguous, allowing for various interpretations to see which one fits the data best.

B: Make a prediction that provides a meaningful value for the unknown population mean.

C: Choosing a random value for the population mean without considering any relevance or connection to the research question, as the goal is merely to generate an arbitrary prediction.

Answer 2

B: Make a prediction that provides a meaningful value for the unknown population mean.

Question 3

True or false: 95% of all samples we could work with will have means that fall within approximately ± 2 standard errors (± the margin of error) of the true population mean.

A: True

B: False

Answer 3

False: It’s not 3, it’s 1.96 👇🏽

95% of all samples we could work with will have means that fall within approximately ± 1.96 standard errors (± the margin of error) of the true population mean.

Question 4

True or false: If we use a normal distribution, the critical
value is 1.96. If we use a t distribution, the critical value depends on the sample size.

A: True

B: False

Answer 4

A: True

> And we calculate a t distribution critical value in Jamovi

Question 5

What is the formula for Margin of Error if we’re using a NORMAL distribution:

A: 1.96 x critical value

B: 1.96 x sample standard deviation

C: 1.96 x standard error

Answer 5

C: 1.96 x standard error

> Answer is in standard error units

Question 6

What are “Common” Estimates:

A: Estimates that fall within the margin of error of the hypothesized population mean are “common” if the hypothesis is true. This kind of estimate (sample mean) supports our hypothesis.

B: Values that are significantly different from the hypothesized population mean, indicating a more accurate representation of the true parameter.

C: Those that consistently fall outside the margin of error, providing stronger evidence against the hypothesis and suggesting a need for revision.

Answer 6

A: Estimates that fall within the margin of error of the hypothesized population mean are “common” if the hypothesis is true. This kind of estimate (sample mean) supports our hypothesis.

Question 7

What does it mean if the estimates are “similar” to the hypothesis?

A: It means there is a lack of reliability in the data, as the margin of error is too wide, making the estimates inconclusive.

B: It suggests a failure to gather diverse data, and the results are biased in favor of the hypothesis, potentially overlooking important variations in the population.

C: It means the estimates fall within the margin of error and the sample means support the hypothesis

Answer 7

C: It means the estimates fall within the margin of error and the sample means support the hypothesis

> This is the same for both normal distributions and t distributions (C.V. x standard error)

> PUT THIS ON YOUR CHEAT SHEET!!! Similar = likely = inside margin of error/ t distribution = estimates support null hypothesis = non-significant = fail to reject the hypothesis = plausible that the null hypothesis is true = p > .05

Question 8

What does it mean if the estimates are “different” from the hypothesis?

A: It means it falls outside of the margin of error and does not support your hypothesis. It means your sample mean refutes your hypothesis.

B: It means there was an error in the data collection process, and the results should be discarded as outliers.

C: It implies a lack of statistical significance, and the hypothesis should be revised to better align with the observed data for more accurate conclusions.

Answer 8

A: It means it falls outside of the margin of error and does not support your hypothesis. It is unlikely and means your sample means refute your hypothesis.

> Estimates outside the margin of error are unlikely (i.e., occur in less than 5% of all samples we could work with) if the hypothesis is true. This kind of estimate (sample mean) REFUTES our hypothesis.

> This is the same for both normal distributions and t distributions (C.V. x standard error)

> PUT THIS ON YOUR CHEAT SHEET!!! Different = unlikely = outside margin of error/ t distribution = estimates refute null hypothesis = statistically significant = reject the null hypothesis =
p < .05

Question 9

The critical value is not always 1.96. When the sample size is larger, the critical value is _____ 1.96

A. Closer to
B. Further away from

Answer 9

A. Closer to

Question 10

Fill in the Significance Testing Flowchart:

A: Step 1: Compare the sample estimate to the hypothesis.

Step 2: Consult an expert opinion: Seek the opinion of an expert in the field to confirm the validity of the hypothesis based on their experience.

Step 3: Accept or reject the hypothesis based on personal judgment: Use personal judgment to decide whether the hypothesis is valid without relying on statistical analysis.

Step 4: Dismiss alternative explanations: Reject alternative explanations for the observed data, insisting that the hypothesis is the only valid interpretation.

B: Step 1 - Specify hypotheses: Propose a value for the
true population parameter.

Step 2 - Design study and collect sample data: Sample data will be used to evaluate the hypothesis.

Step 3: Assess the similarity of data and hypothesis: Compare sample estimate to hypothesis.

Step 4: Make a judgment about the hypothesis: The estimate is either similar to or different from the hypothesis

C: Step 1: Compare the sample estimate to the hypothesis.

Step 2: Choose the hypothesis that seems more plausible: Select the hypothesis that appears more reasonable based on subjective judgment rather than statistical evidence.

Step 3: Disregard statistical significance: Ignore statistical tests and significance levels, and accept the hypothesis that aligns with preconceived notions or expectations.

Step 4: Avoid peer review: Skip the peer-review process and immediately accept the hypothesis, disregarding external input and critique.

Answer 10

B: Step 1 - Specify hypotheses: Propose a value for the
true population parameter.

Step 2 - Design study and collect sample data: Sample data will be used to evaluate the hypothesis.

Step 3: Assess the similarity of data and hypothesis: Compare sample estimate to hypothesis.

Step 4: Make a judgment about the hypothesis: The estimate is either similar to or different from the hypothesis

Question 11

If you determine that the results are “non-significant” what does it mean?

A: It indicates a flaw in the research methodology, and the data should be dismissed as unreliable. The hypothesis is likely incorrect due to these methodological issues.

B: It suggests that the study lacked statistical power, and repeating the experiment with a larger sample size would likely yield significant results, confirming the hypothesis.

C: The hypothesized population could have produced the data

Answer 11

C: The hypothesized population could have produced the data

> You fail to reject the hypothesis

Question 12

If you determine that the results are “statistically significant” what does it mean?

A: It suggests a flaw in the experimental design, and further investigation is needed to identify and correct the sources of bias. The hypothesis may be valid with adjustments.

B: The hypothesized population is unlikely to have produced the data

C: It indicates that the study may have unintentionally manipulated the data, and the findings should be considered dubious. The hypothesis might be accurate, but caution is warranted due to potential biases.

Answer 12

B: The hypothesized population is unlikely to have produced the data

> You reject the hypothesis

Question 13

What is an “alternate hypothesis?”

A: The alternate (alternative) hypothesis is a prediction that often aligns with the idea that “something is happening”.

B: The alternate hypothesis is a statement suggesting that the observed results are due to chance or random fluctuations in the data, rather than indicating a real effect.

C: An alternate hypothesis is a conjecture proposing that the experimental conditions have no impact on the outcome, and any observed effects are merely coincidental or irrelevant to the study

Answer 13

A: The alternate (alternative) hypothesis about the population mean that reflects the researcher’s interests or beliefs. A prediction that often aligns with the idea that “something is happening”.

> Ha = alternate/alternative hypothesis

Question 14

What is a One-Tailed Alternate Hypotheses?

A: Used when researchers anticipate ambiguous or unpredictable outcomes, allowing for the possibility of both an increase and a decrease in the observed results.

B: Researchers make predictions about the expected results in both directions, assuming that the outcome could either increase or decrease, depending on various factors.

C: Researchers specify one-tailed hypotheses when the expected results can only go in one direction (an increase or a decrease, not both)

Answer 14

C: An alternate hypothesis where the researcher expects or predicts an increase or a decrease, but not both. Researchers specify one-tailed hypotheses when the expected results can only go in one direction (an increase or a decrease, not both).

> Example: If the study goal is to examine whether people tend to maintain a humorous perspective even in the face of stress or adversity, the alternate hypothesis is that the population mean rating should be greater than “sometimes true.”

I use a one-tailed hypothesis because I expect that the
population mean can be higher than 3 but not lower than 3

Ha : μ > 3

OR: The alternate hypothesis also can be that the population mean rating should be smaller than
“sometimes true.”

Ha : μ < 3

Question 15

What is a Two-Tailed Alternate Hypotheses?

A: Applied when researchers expect a precise and specific outcome, either an increase or a decrease, and want to cover all possible scenarios.

B: Researchers focus on predicting only one direction of the results, either an increase or a decrease, excluding the possibility of an outcome in the opposite direction.

C: Researchers use two-tailed hypotheses when the results can reasonably go in either direction (scores can increase or decrease).

Answer 15

C: An alternate hypothesis where the researcher expects or predicts that either an increase or a decrease are possible. Researchers use two-tailed hypotheses when the results can reasonably go in either direction (scores can increase or decrease).

> Example: Suppose the study aims to explore whether
people tend to maintain either a humorous perspective or a humorless perspective.

The true mean rating in the population could be greater than or less than “sometimes true.”

Ha : μ > 3 or μ < 3 OR: Ha : μ ≠ 3

> While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables.

Question 16

What is a Null Hypothesis?

A: The null hypothesis is a prediction that aligns with the researcher’s expectations and supports the idea that a significant effect or change is occurring in the study.

B: The null hypothesis is a value opposite of what
the researcher expects. A value that often aligns
with the idea that “nothing is happening”

C: In a null hypothesis, researchers propose a value that is in line with their anticipated outcomes, indicating that the experimental conditions are likely to produce a noticeable effect.

Answer 16

B: The null hypothesis about the population mean is a value opposite of what the researcher expects. A value that often aligns with the idea that “nothing is happening.”

> Example: The true population mean rating is “sometimes true.”

H0 : μ = 3

> Our goal is ALWAYS to prove that the null hypothesis is not true. We want to reject the hypothesis!

> The goal of a hypothesis test is to show that the null
hypothesis is probably false.

> The null hypothesis is innocent until proven guilty.

> We also cannot prove the null hypothesis is true (you can NEVER accept the null hypothesis) (perhaps we fail to reject the null hypothesis due to the small sample size). We only can state that the null hypothesis is PLAUSIBLE (remember the alien example she gave in class).

> While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables.

Question 17

What role does the sample mean (estimates) play in hypothesis testing?

A: The sample mean will be used to determine whether the data can refute the null

B: The sample mean serves as an absolute confirmation of the null hypothesis, providing direct evidence that the expected outcome has occurred as predicted.

C: The sample mean acts as an independent measure, separate from the null hypothesis, and is not relevant in assessing the validity of the null hypothesis.

Answer 17

A: The sample mean will be used to determine
whether the data can refute the null

Question 18

Standard Error Revisited: What is standard error?

A: The standard error is the standard deviation of
estimates from many different random samples

B: The standard error represents the average difference between the estimated value and the true population parameter, providing a measure of accuracy in the data.

C: Standard error is a measure of variability within a single sample, indicating the spread of data points around the sample mean, rather than across multiple random samples.

Answer 18

A: The standard error is the standard deviation of
estimates from many different random samples

Question 19

If the estimate is outside of the margin of
error, it ______

A. Refutes the null hypothesis
B. Supports the null hypothesis

Answer 19

A. Refutes the null hypothesis

Question 20

What is a t statistic?

A: The t statistic is an arbitrary measure used to evaluate the reliability of an estimate, without considering its distance from the null hypothesis or its location in the sampling distribution.

B: A t statistic is a raw score that directly represents the estimate’s value in relation to the null hypothesis, without any standardization or consideration of standard error units.

C: The t statistic is a standardized estimate. It gives an estimate’s distance to the null hypothesis on a standardized metric like a z-score. A t statistic conveys the location of an estimate in the sampling distribution in standard error units

Answer 20

C: The difference between the sample mean and the
hypothesized population mean in standard error units. Exactly like a z score but applied to an estimate rather than an individual’s score.The t statistic is a standardized estimate. It gives an estimate’s distance to the null hypothesis on a standardized metric like a z-score. A t statistic conveys the location of an estimate in the sampling distribution in standard error units

t = x̄ - μ ÷ sx̄ (put all equations on your cheat sheet)

Which translates to:
t = Sample estimate - Hypothesis (population mean) ÷ Standard error

Example with interpretation (put all interpretation examples on your cheat sheet):
> A sample mean of 3.26 is +2.77 standard error units higher than the hypothesized mean of 3.

t = x̄ - μ ÷ sx̄ 👉🏽 t = 3.26 - 3 ÷ 0.094 = 2.77 > 1.979

The difference is about 2.77 times as large as what we would expect due to sampling error alone (due to random chance).

The t statistic (2.77) is larger than the C.V. (1.979). It indicates that the sample mean is outside of the margin of error.

> And this would be the same if the answer turned out to be -2.77 as well, because we’re clearly working with a two-tailed hypothesis so it can either be positive or negative, and -2.77 is still outside of the margin of error (+- 1.979).

Question 21

Rule of thumb:

True or false: If the null hypothesis is true, 95% of all samples we could work with fall within about (should have a t statistic between about) ± 1.979 (determined by sample size) standard errors of μ.

A: True

B: False

Answer 21

A: True

Question 22

On a standardized t metric, the sample mean is 2.77 standard errors from a population mean under the null hypothesis. Can the estimate refute the null hypothesis that the true population mean rating is “sometimes true”?

A. Yes
B. No

Answer 22

A. Yes

Question 23

What is a probability value (p-value):

A: Probability value reflects the absolute certainty of an estimate’s accuracy, with a high probability indicating complete confidence in the estimate’s alignment with the hypothesis.

B: Researchers use probability values to gauge the
similarity of an estimate to a hypothesis. A high probability means the estimate is similar to, common under the hypothesis. It’s inside the margin of error. A low probability means the estimate is different, rare, or too extreme. It’s outside the margin of error.

C: A probability value represents the likelihood that the estimate is entirely inaccurate, with a low probability indicating a high probability of error in the estimate.

Answer 23

B: Researchers use probability values to gauge the
similarity of an estimate to a hypothesis. Assuming that the null hypothesis is true, how likely is such a population to have produced a sample mean at least as different as the one from the data.

A high probability means the estimate is similar to, common under the hypothesis. It’s inside the margin of error.

A low probability means the estimate is different, rare, or too extreme. It’s outside the margin of error.

Question 24

What do the p-values (p > .05) and (p < .05) mean?

A: p > .05 = non-significant. This means that the hypothesized population could have produced the data; fail to reject the null hypothesis.

p < .05 = statistically significant. This means that the hypothesized population is unlikely to have produced the data; reject the null hypothesis.

B: p > .05 = statistically significant. This means that the hypothesized population is likely to have produced the data; reject the null hypothesis.

p < .05 = non-significant. This means that the hypothesized population is unlikely to have produced the data; fail to reject the null hypothesis.

Answer 24

A: p > .05 = non-significant. This means that the hypothesized population could have produced the data; fail to reject the null hypothesis.

p < .05 = statistically significant. This means that the hypothesized population is unlikely to have produced the data; reject the null hypothesis.

Question 25

What are exact probability values? A: Represent the probability of obtaining the exact same mean or t statistic in repeated samples, assuming that the null hypothesis is false. B: Assuming the null hypothesis is true, exact probability values (p values) indicate the likelihood of obtaining a mean or t statistic in a single sample, without consideration for the distribution of means in repeated samples. C: Assuming that the null hypothesis is true, p (p value) is the proportion of samples that would give a mean (or t statistic) at least as extreme as the one from the data

Answer 25

C: Assuming that the null hypothesis is true, p (p value) is the proportion of samples that would give a mean (or t statistic) at least as extreme as the one from the data > It might be helpful to look at the image on slide 62. The gray area represents the p-values in a two-tailed hypothesis. And here's an interpretation example for a two-tailed hypothesis (PUT THIS ON YOUR CHEAT SHEET): > Ha : μ ≠ 3 > p(t ≥ 2.77 or t ≤ - 2.77 | H0 is true) = 0.006 > 0.006 is the p-value that you'll split in two, placing p=0.003 on the left and right side of the two-tailed graph > If the population mean is exactly “sometimes true”, the probability of working with a sample that gives a t statistic beyond or equal to ± 2.77 is 0.006 > Since the p-value = 0.006 is < 0.5 it would be considered statistically significant. It's a low probability, placing it outside of the margin of error, allowing you to reject the null hypothesis > A t-distribution and a p-value should give you the same outcome And here's an interpretation example for a one-tailed hypothesis (PUT THIS ON YOUR CHEAT SHEET): > Ha : μ > 3 > p(t ≥ 2.77 | H0 is true) = 0.003 > t = 2.77 > 0.003 is the p-value that you will place on the right side only since we're only looking at ≥ > If the population mean is exactly “sometimes true”, the probability of working with a sample that gives a t statistic greater than or equal to 2.77 is 0.003 > Since the p-value = 0.003 is < 0.5 it would be considered statistically significant. It's a low probability, placing it outside of the margin of error, allowing you to reject the null hypothesis And here's another interpretation example for a one-tailed hypothesis (PUT THIS ON YOUR CHEAT SHEET): > Ha : μ < 3 > p(t ≤ 2.77 | H0 is true) = 0.997 > t = 2.77 > 0.997 is the p-value that you will place on the left side only since we're only looking at ≤ > If the population mean is exactly “sometimes true”, the probability of working with a sample that gives a t statistic smaller than or equal to 2.77 is 0.997 > Since the p-value = 0.997 is > 0.5 it would be considered non-significant. It's a high probability, placing it inside of the margin of error, so you'd have to fail to reject the null hypothesis > I think it would be helpful to put these images on your cheat sheet (slides 62-71)

Question 26

True or false: Whether you're dealing with a one-tailed or two-tailed hypothesis the only things that will change are the alternate hypothesis and p-values. The population mean and t-distribution values will not change. A: True B: False

Answer 26

A: True

Question 27

When writing out interpretations you'll see a vertical pipe written out that looks like this |, what does it mean? A: The vertical pipe | = it's just a way to separate data B: The vertical pipe | = "absolute value." C: The vertical pipe | = "assuming that" or "conditional on."

Answer 27

C: The vertical pipe | = "assuming that" or "conditional on." > The p-value is a conditional probability because it reflects the chance of obtaining the sample data from a population where the null is true p(data like ours | H0 is true in the population) You should out this on your CHEAT SHEET!!!

Question 28

True or false: The one-tailed and two-tailed hypotheses produce different p-values even with the same dataset. A. True B. False

Answer 28

A. True

Question 29

True or false: P-values, t-statistics, and confidence intervals/margins of error will all lead you to the same conclusion - informing you to either reject or fail to reject the null hypothesis. A: True B: False

Answer 29

A: True

Question 30

Why .05 or 5%? A: It's a mathematical law B: Because R.A. Fisher — an influential biologist and statistician — said so C: Because 95% falls within the margin of error and 5% fall outside the margin of error

Answer 30

B: Because R.A. Fisher — an influential biologist and statistician — said so

Question 31

If p > .05 A: Fail to reject the null hypothesis (we cannot claim that the null hypothesis is true!). Results are non-significant because the sample mean is not that different from the hypothesis (the t statistic is within the critical values and the sample mean is within the margin of error). B: Refute the null hypothesis. Results are significant because the sample mean is substantially different from the hypothesis (the t statistic is outside the critical values and the sample mean is outside the margin of error).

Answer 31

A: Fail to reject the null hypothesis (we cannot claim that the null hypothesis is true!). Results are non-significant because the sample mean is not that different from the hypothesis (the t statistic is within the critical values and the sample mean is within the margin of error).

Question 32

If p < .05 A: Fail to reject the null hypothesis (we cannot claim that the null hypothesis is true!). Results are non-significant because the sample mean is not that different from the hypothesis (the t statistic is within the critical values and the sample mean is within the margin of error). B: Refute the null hypothesis. Results are significant because the sample mean is substantially different from the hypothesis (the t statistic is outside the critical values and the sample mean is outside the margin of error).

Answer 32

B: Refute the null hypothesis. Results are significant because the sample mean is substantially different from the hypothesis (the t statistic is outside the critical values and the sample mean is outside the margin of error).

Question 33

More interpretations you might want to add to your cheat sheet:

Answer 33

Interpretation #1: Ha : μ > 3 This is a one-tailed hypothesis. The sample mean is 3.26 and t = 2.77 A sample mean of 3.26 (or t = 2.77) or more extreme is not common for a population whose mean is “sometimes true”. Hence, the sample mean is significantly different from 3, so the difference between the data and the null hypothesis is unlikely due to sampling error. The null hypothesis can be refuted. People tend to maintain a humorous perspective even in the face of stress or adversity. Interpretation #2: Ha : μ ≠ 3 This is a two-tailed hypothesis The sample mean is 3.26 and t = 2.77 A sample mean of 3.26 (or t = 2.77) or more extreme is not common for a population whose mean is “sometimes true”. Hence, the sample mean is significantly different from 3, so the difference between the data and the null hypothesis is unlikely due to sampling error. The null hypothesis can be refuted. People tend to maintain either a humorous perspective or a humorless perspective even in the face of stress or adversity. Interpretation #3: Ha : μ < 3 This is a one-tailed hypothesis The sample mean is 3.26 and t = 2.77 A sample mean of 3.26 (or t = 2.77) or even smaller is common for a population whose mean is “sometimes true”. Hence, the sample mean is not significantly different from 3. We fail to reject the null hypothesis. We never can accept the null hypothesis but it is plausible that the population mean is “sometimes true."

Question 34

Confidence Intervals And Significance Tests: A: B: Significance tests can also be performed using confidence intervals. If the hypothesized population mean falls within the 95% confidence interval, the null hypothesis is not plausible, you can reject the null hypothesis. If the hypothesized population mean is not in the interval, it is plausible, you fail to reject the null hypothesis. We focus on C.I. for the two-tailed hypothesis. B: Significance tests can also be performed using confidence intervals. If the hypothesized population mean falls within the 95% confidence interval, the null hypothesis is plausible. If the hypothesized population mean is not in the interval, it is significant. We focus on C.I. for the two-tailed hypothesis.

Answer 34

B: Significance tests can also be performed using confidence intervals. If the hypothesized population mean falls within the 95% confidence interval, the null hypothesis is plausible. If the hypothesized population mean is not in the interval, it is significant. We focus on C.I. for the two-tailed hypothesis.

Question 35

What is the formula for 95% confidence interval using critical values vs. the basic 1.96. A: 95% C.I. = sample estimate ± (C.V. + standard error) Which translates to sample estimate ± margin of error B: 95% C.I. = sample estimate ± (C.V. x standard error) Which translates to sample estimate ± margin of error

Answer 35

B: 95% C.I. = sample estimate ± (C.V. x standard error) Which translates to sample estimate ± margin of error Interpretation example: > 95% C.I. = sample estimate ± (C.V. x standard error) > = 3.26 ± (1.979 x .094) = 3.26 ± .186 (this is the margin of error) > 3.26 ± .186 = [3.07, 3.45] these are the critical values, lower and upper bound > We are 95% confident that the interval (range) from 3.07 to 3.45 includes the true mean humor rating from the full population *** Important note for Jamovi!!! For hypothesis testing with confidence intervals, you need to change the "Test Value" to 0 even though the null hypothesis H0 : μ = 3 BUT to find the t-statistic and p-value the "Test Value" needs to be 3 so when you change the "Test Value" to 0 remember to only collect the 95% confidence interval data and then change the "test value" to 3 when you want to collect the t-statistic and p-value data!!!!

Question 36

When the p-value is larger than 0.05, we _______ A. Reject the null hypothesis B. Fall to reject the null hypothesis C. Accept the null hypothesis

Answer 36

B. Fall to reject the null hypothesis

Question 37

What are the three equivalent ways to test the null hypothesis? A: t-statistic, standard error, confidence interval B: standard deviation, t-statistic, p-value C: t-statistic, p-value, and confidence interval

Answer 37

C: t-statistic, p-value, and confidence interval 1. t statistic: Compare with critical value - if larger or smaller than the critical value it’s significant 2. p-value: Compare with 0.05 - if larger than 0.05 it’s not significant - if it’s smaller than 0.05 it’s significant 3. Confidence interval: If it covers the null hypothesis it’s not significant - if it does not cover the null hypothesis then it’s significant NOTE: Just note that all three methods must be consistent with one another. If one method rejects the null, then all of them should reject the null. If one method fails to reject the null, then all of them should fail to reject the null.

Question 38

Jamovi one-sample t test confidence intervals, t-statistics, and p-values: True or false: If we want a confidence interval for our sample mean, we must always set the “test value” equal to zero and then ignore the t-statistic and p-value that appear in the table next to the confidence interval because they are incorrect. If we want a t-statistic and p-value, we must set the “Test value” equal to the population mean we assume under the null hypothesis and then ignore the lower and upper bounds of the confidence interval that appear in the table next to the t-statistic and p-value because they are incorrect. A: True B: False

Answer 38

A: True

Question 39

Jamovi one-sample t test one-sided hypothesis test, t-statistic and p-value: True or false: When we switch between two-sided and one-sided hypothesis tests we will notice that the t-statistic will remain the same but the p-value will change. A: True B: False

Answer 39

A: True For example, if our one-sided hypothesis test is Ha > 3 our p-value will be half the size of the two-sided test's p-value because we are now only looking at the probability on the right tail of the distribution.

Question 40

In Jamovi, for a one-sample t-test, what are the steps to find critical values: A: Click "distrACTION," then "T-Distribution." Check "Compute quantile(s), change p = to 0.95, and check "central interval quantiles. Hit enter and find your x1 and x2 values, these are your critical values. B: Determine degrees of freedom, click "distrACTION," then "T-Distribution." Enter degrees of freedom, check "Compute quantile(s), change p = to 0.95, and check "central interval quantiles. Hit enter and find your x1 and x2 values, these are your critical values. C: Click "distrACTION," then "T-Distribution." Check "Compute quantile(s), change p = to 0.05, and check "central interval quantiles. Hit enter and find your x1 and x2 values, these are your critical values.

Answer 40

B: Determine degrees of freedom, click "distrACTION," then "T-Distribution." Enter degrees of freedom, check "Compute quantile(s), change p = to 0.95, and check "central interval quantiles. Hit enter and find your x1 and x2 values, these are your critical values. ADD THIS TO YOUR CHEAT SHEET!!!

Question 41

In Jamovi, for a one-sample t-test, what are the steps to find a t-statistic and p-value: A: Choose “Analyses,” “T-Tests,” and then “One Sample T-Test.” Move the desired variable over to the "Dependent Variables" box. Under the “Hypothesis” section, enter zero into the box next to “Test Value.” Then choose either ≠ , >, or <. Hit enter. "Statistic" is your t-statistic and "p" is your p-value. B: Choose “Analyses,” “T-Tests,” and then “One Sample T-Test.” Move the desired variable over to the "Dependent Variables" box. Under the “Hypothesis” section, enter your alternate hypothesis value into the box next to “Test Value.” Then choose either ≠ , >, or <. Hit enter. "Statistic" is your t-statistic and "p" is your p-value. C: Choose “Analyses,” “T-Tests,” and then “One Sample T-Test.” Move the desired variable over to the "Dependent Variables" box. Under the “Hypothesis” section, enter your population mean into the box next to “Test Value.” Then choose either ≠ , >, or <. Hit enter. "Statistic" is your t-statistic and "p" is your p-value.

Answer 41

C: Choose “Analyses,” “T-Tests,” and then “One Sample T-Test.” Move the desired variable over to the "Dependent Variables" box. Under the “Hypothesis” section, enter your population mean into the box next to “Test Value.” Then choose either ≠ , >, or <. Hit enter. "Statistic" is your t-statistic and "p" is your p-value. ADD THIS TO YOUR CHEAT SHEET!!!

Question 42

In Jamovi, for a one-sample t-test, what are the steps to find a confidence interval: A: Choose “Analyses,” “T-Tests,” and then “One Sample T-Test.” Move the desired variable over to the "Dependent Variables" box. Under the “Hypothesis” section, enter your population mean into the box next to “Test Value.” Then choose either ≠ , >, or <. Select "Mean difference" and "Confidence interval." Hit enter. Find your lower and upper bound 95% confidence interval. You can also gather the t-statistic and p-value at the same time. B: Choose “Analyses,” “T-Tests,” and then “One Sample T-Test.” Move the desired variable over to the "Dependent Variables" box. Under the “Hypothesis” section, enter zero into the box next to “Test Value.” Then choose either ≠ , >, or <. Select "Mean difference" and "Confidence interval." Hit enter. Find your lower and upper bound 95% confidence interval. Notice that your t-statistic and p-value are now incorrect since you changed your "Test value" to zero. Do not use these values! C: Choose “Analyses,” “T-Tests,” and then “One Sample T-Test.” Move the desired variable over to the "Dependent Variables" box. Under the “Hypothesis” section, enter one into the box next to “Test Value.” Then choose either ≠ , >, or <. Select "Mean difference" and "Confidence interval." Hit enter. Find your lower and upper bound 95% confidence interval. Notice that your t-statistic and p-value are now incorrect since you changed your "Test value" to zero. Do not use these values!

Answer 42

B: Choose “Analyses,” “T-Tests,” and then “One Sample T-Test.” Move the desired variable over to the "Dependent Variables" box. Under the “Hypothesis” section, enter zero into the box next to “Test Value.” Then choose either ≠ , >, or <. Select "Mean difference" and "Confidence interval." Hit enter. Find your lower and upper bound 95% confidence interval. Notice that your t-statistic and p-value are now incorrect since you changed your "Test value" to zero. Do not use these values! ADD THIS TO YOUR CHEAT SHEET!!!

Question 43

True or false: In Jamovi, to switch between a two-sided and one-sided one-sample t-test under “Analyses,” “T-Tests,” and “One Sample T-Test” all we need to do is change the test value under hypothesis to either < or >? A: True B: False

Answer 43

A: True ADD THIS TO YOUR CHEAT SHEET!!!

Question 44

Assignment 3: This is basically just interpreting a confidence interval. The values from the assignment don't really matter. It's the interpretation that matters. Which of the following interpretations is correct for the confidence interval? a) If another study replicates this study, it is 95% likely that the new sample mean would fall in the range of 623 to 641 b) 95% of all random samples would yield confidence intervals between 623 to 641 c) We are 95% confident that the range (623 to 641) includes the true population average number of social ties per person in the United States d) The true population average number of social ties per person in the United States must fall within the range of 623 to 641

Answer 44

c) We are 95% confident that the range (623 to 641) includes the true population average number of social ties per person in the United States This is basically just interpreting a confidence interval. The values from the assignment don't really matter. It's the interpretation that matters.

Question 45

Assignment 3: This is basically just interpreting a t-statistic. The values from the assignment don't really matter. It's the interpretation that matters. Which of the following interpretations is correct for the t-statistic 0.52? a) A sample of 171 adults should produce a sample mean that differs from the population mean by 0.52 points, on average b) On a standardized metric, the sample mean is 0.52 times larger than the hypothesized population mean c) The difference between the sample mean and the hypothesized population mean is about 0.52 times larger than what you would expect due to sampling error d) The sample mean is about 0.52 times larger than the hypothesized population mean

Answer 45

c) The difference between the sample mean and the hypothesized population mean is about 0.52 times larger than what you would expect due to sampling error This is basically just interpreting a t-statistic. The values from the assignment don't really matter. It's the interpretation that matters.

Question 46

Assignment 3: This is basically just interpreting a p-value. The values from the assignment don't really matter. It's the interpretation that matters. The probability value (p-value) for the t-test is 0.604. Which of the following interpretations is correct? a) The probability of observing a sample of 171 adults with a t-statistic value of 0.52 is 0.604 b) If the population average number of social ties per person is 630, the probability of selecting a sample of 171 adults that shows a t-statistic value of 0.52 is 0.604 c) If the population average number of social ties per person is 630, the probability of selecting a sample of 171 adults that shows a t-statistic value of 0.52 or more extreme is 0.604 d) The probability that the null hypothesis is true is 0.604

Answer 46

c) If the population average number of social ties per person is 630, the probability of selecting a sample of 171 adults that shows a t-statistic value of 0.52 or more extreme is 0.604 This is basically just interpreting a p-value. The values from the assignment don't really matter. It's the interpretation that matters.