Quiz 8 - Chapter 8: Hypothesis Testing Flashcards
A researcher is studying the happiness of college students. On a happiness scale that ranges from 0 to 100, they want to test if the population mean happiness rating is different from 70 (i.e., the null hypothesis is μ = 70 and the alternative hypothesis is μ ≠70).
To do this, they collect a sample of 250 students from UCLA and measure their happiness levels. They find a sample mean happiness level of 65, and they estimate the standard error of the mean to be 5. What would the t-statistic be for this study?
-1
I found this answer by following this t-statistic formula:
t = x̄ - μ ÷ sx̄
t = 65 - 70 ÷ 5 = -1
PUT ALL FORMULAS ON YOUR CHEAT SHEET!!!
The p-value for the happiness study described in the previous question was .318 (the null hypothesis is μ = 70 and the alternative hypothesis is μ ≠70).
Given the t-statistic and p-value in Question 1, if the researcher had instead wanted to test if the population mean happiness rating was less than 70 (i.e., the alternative hypothesis is μ < 70), what would the corresponding p-value be?
0.159
She never taught us how to do this so I found a formula online and approved it with the TAs. So, use the following formula:
If p = .318 in a two-tailed hypothesis and you’re switching to a one-tailed hypothesis with a POSITIVE t-statistic all you need to do to find the > p-value is divide .318 by 2 and your new p-value will be 0.159.
To find your one-tailed p-value that’s < do the following:
1 - (.318 ÷ 2) = 0.841
HOWEVER, since we have a NEGATIVE t-statistic we need to flip these answers!!! Now < = 0.159 and > = 0.841
And always remember that the < and > p-values must always be equal to 1 (0.159 + 0.841 = 1
The p-value for the happiness study described in the previous question was .318 (the null hypothesis is μ = 70 and the alternative hypothesis is μ ≠70).
Given the t statistic and p-value in Question 1, if the researcher had instead wanted to test if the population mean happiness rating was greater than 70 (i.e., the alternative hypothesis is μ > 70), what would the corresponding p-value be?
0.841
She never taught us how to do this so I found a formula online and approved it with the TAs. So, use the following formula:
If p = .318 in a two-tailed hypothesis and you’re switching to a one-tailed hypothesis with a POSITIVE t-statistic all you need to do to find the > p-value is divide .318 by 2 and your new p-value will be 0.159.
To find your one-tailed p-value that’s < do the following:
1 - (.318 ÷ 2) = 0.841
HOWEVER, since we have a NEGATIVE t-statistic we need to flip these answers!!! Now < = 0.159 and > = 0.841
And always remember that the < and > p-values must always be equal to 1 (0.159 + 0.841 = 1
A researcher assumes that the college entrance exam has a mean of 300 in the population. A sample has 100 applicants with a mean of 310. Which of the following null hypotheses is most appropriate for this scenario?
A: The population average college entrance exam score equals 310
B: The sample average college entrance exam score equals 310
C: The population average college entrance exam score equals 300
D: The sample average college entrance exam score equals 300
C: The population average college entrance exam score equals 300
A researcher assumes that the college entrance exam has a mean of 300 in the population. A sample has 100 applicants with a mean of 310. We conduct a hypothesis test to determine whether the sample mean is significantly different from the hypothesized population mean. The two-tailed probability value (p-value) for the analysis is p = .08. Which of the following interpretations is correct regarding the probability value?
A: If the population mean is 300, there is an 8% probability of obtaining a sample mean of 310 or larger
B: If the population mean is 300, there is an 8% probability of obtaining a sample mean of exactly 300
C: There is an 8% probability that the null is true
D: If the population mean is 300, there is an 8% probability of obtaining a sample mean of 310 or larger or 290 or smaller
E: If the population mean is 300, there is an 8% probability of obtaining a sample mean of exactly 310
D: If the population mean is 300, there is an 8% probability of obtaining a sample mean of 310 or larger or 290 or smaller
Following the 5th question, can we change to the one-tailed significance test after we find that the two-tailed significance test is nonsignificant? Check all that apply
A: Yes, we can because the process is flexible.
B: No, we cannot because we cannot take advantage of the data.
C: Yes, we can because our goal is to obtain significant results.
D: No, we cannot because we need to make assumptions before we conduct hypothesis testing.
B: No, we cannot because we cannot take advantage of the data.
D: No, we cannot because we need to make assumptions before we conduct hypothesis testing.
It is assumed that a college entrance exam has a population mean of 300. College A has a mean of 280, and College B has a mean of 310. Considering a two-tailed test, which sample will produce the larger probability value (p-value)?
A: The sample with a mean of 280
B: The sample with a mean of 310
B: The sample with a mean of 310
A clinical researcher assumes that the population rate of clinical depression among new mothers is at 10% (the null hypothesis). Believing that the true average depression rate among new mothers in the population is smaller than 10%, the researchers conduct a one-tailed hypothesis test where the expected direction of the effect is lower than 10%. Which of the following corresponds to the alternate hypothesis for the test?
A: The sample rate of clinical depression < 10%
B: The population rate of clinical depression < 10%
C: The sample rate of clinical depression > 10%
D: The population rate of clinical depression > 10%
E: The population rate of clinical depression is 10%
F: The sample rate of clinical depression is 10%
B: The population rate of clinical depression < 10%
This is true because everything is being compared to the null hypothesis which refers to the population
A clinical researcher assumes that the population rate of clinical depression among new mothers is at 10% (the null hypothesis). Believing that the population depression rate among new mothers is smaller than 10%, the researchers conduct a one-tailed hypothesis test where the expected direction of the effect is lower than 10%. Which of the following means is most likely to produce a significant finding?
A: 15%
B: 10%
C: 100%
D: 8%
D: 8%
Which of the following methods allows a researcher to test the null hypothesis? Check all that apply.
A: Looking at only the standard error value
B: Looking at p-values
C: Constructing confidence intervals
D: Calculating t statistics
B: Looking at p-values
C: Constructing confidence intervals
D: Calculating t statistics
Imagine that a researcher calculates a t-statistic of 3.5. Which of the following is/are correct interpretation(s) of the t-statistic?
A: The sample mean is 3.5 standard error units lower than the hypothesized mean.
B: The difference between the sample and hypothesized mean is about 3.5 times as large as what we would expect from sampling error.
C: The sample mean is 3.5 standard deviation units higher than the hypothesized mean.
D: The sample mean is 3.5 standard error units higher than the hypothesized mean.
E: The difference between the sample and hypothesized mean is 3.5 times the size of the sample standard deviation.
B: The difference between the sample and hypothesized mean is about 3.5 times as large as what we would expect from sampling error.
D: The sample mean is 3.5 standard error units higher than the hypothesized mean.
Which of the following is correct interpretation of p-value?
A: The probability of obtaining results as extreme as the one from the data, assuming that the null hypothesis is true
B: The probability of obtaining results as extreme as the one from the data or more extreme, assuming that the null hypothesis is true.
C: The probability that our hypothesis is wrong.
D: The probability that our hypothesis is correct.
B: The probability of obtaining results as extreme as the one from the data or more extreme, assuming that the null hypothesis is true.
In a two-sided test, the result is statistically significant. Knowing this conclusion, what can you say about this test? CHECK ALL THAT APPLY:
A: The 95% confidence interval did not contain the hypothetical population mean
B: The 95% confidence interval contained the hypothetical population mean
C: The absolute value of the t-statistic was less than the critical value
D: The p-value was greater than .05
E: The p-value was less than or equal to .05
F: The absolute value of the t-statistic was greater than or equal to the critical value
A: The 95% confidence interval did not contain the hypothetical population mean
E: The p-value was less than or equal to .05
F: The absolute value of the t-statistic was greater than or equal to the critical value
A researcher wants to test whether one mean is significantly larger than the null hypothesis of 10. They conduct one-tailed t-test and found a p-value that is 0.54. What would be the appropriate conclusion they should make from the results of this test?
A: They should accept the alternative hypothesis.
B: They should fail to reject the alternative hypothesis.
C: They should reject the null hypothesis.
D: They should fail to reject the null hypothesis.
D: They should fail to reject the null hypothesi
True or false? A null hypothesis can be proven true.
A: True
B: False
B: False
