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BA 216 📊 > More hypothesis testing °❀⋆.ೃ࿔*:･ > Flashcards

More hypothesis testing °❀⋆.ೃ࿔*:･ Flashcards

1
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A
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2
Q

What is the null hypothesis (H0)?

A

Responses are equivalent to random guesses

H0 (pronounced H-naught) represents the status-quo in hypothesis testing.

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3
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What is the alternative hypothesis (HA)?

A

People have knowledge that helps them do better than random guessing or false knowledge leading to worse performance

HA (pronounced H-A) represents a new or stronger perspective.

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4
Q

What percentage of correct answers would you expect from random guessing with three options?

A

33.3333%

This is derived from having one correct answer out of three options.

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5
Q

What is the basic framework of a hypothesis test?

A

It involves the null hypothesis (H0) and the alternative hypothesis (HA) to determine if there is evidence against H0

The framework starts with skepticism towards the alternative hypothesis.

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6
Q

True or False: Failing to reject the null hypothesis means it is true.

A

False

Failing to reject H0 means there isn’t strong evidence against it, but does not confirm its truth.

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7
Q

What does it mean to fail to reject the null hypothesis?

A

It means the evidence for the alternative hypothesis is weak

It does not imply that the null hypothesis is accepted as true.

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8
Q

What is a key part of the scientific method in hypothesis testing?

A

Starting from the position of a skeptic

The null hypothesis is considered the real one until strong evidence suggests otherwise.

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9
Q

What is the purpose of hypothesis testing?

A

To determine if there is enough evidence to reject the null hypothesis

Hypothesis testing helps in making conclusions about population parameters.

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10
Q

What is the notation for the population parameter in hypothesis testing?

A

It is written as ‘p’

This notation represents the proportion of the population that meets the criteria of the hypothesis.

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11
Q

What does a p-value indicate?

A

The strength of evidence against the null hypothesis

A lower p-value suggests stronger evidence against H0.

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12
Q

What is a confidence interval?

A

A range of values that estimates the population parameter with a certain level of confidence

It helps in understanding the variability and uncertainty in sample estimates.

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13
Q

What is the critical value for a 95% confidence interval based on the z-score?

A

It is determined through statistical tables

The critical value is used to calculate the margin of error for the confidence interval.

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14
Q

What is the point estimate in hypothesis testing?

A

It is the sample proportion (p-hat)

Point estimate serves as a best guess for the population parameter based on sample data.

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15
Q

Fill in the blank: The jury considers whether the evidence is so convincing that there is no reasonable doubt regarding the person’s _______.

A

guilt

This analogy illustrates hypothesis testing in a legal context.

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16
Q

What does it mean if the null value falls within the range of plausible values from the confidence interval?

A

We cannot say the null value is implausible

This indicates insufficient evidence to reject the null hypothesis.

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17
Q

What is the sample size in the example about college-educated adults answering the vaccination question?

A

50

This is the number of respondents considered in the hypothesis testing example.

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18
Q

What is p-hat in hypothesis testing?

A

The sample proportion of respondents who answered correctly

This helps in estimating the population parameter for hypothesis testing.

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19
Q

What is the significance of the central limit theorem in hypothesis testing?

A

It allows for the approximation of the sampling distribution of the sample mean

This theorem is crucial for ensuring the validity of hypothesis tests when sample sizes are large.

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20
Q

What is the standard error often computed differently in the context of?

A

Hypothesis test for a proportion

The standard error can vary depending on the test being conducted.

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21
Q

What conclusion can we draw if the data do not provide sufficient evidence to reject H0?

A

Fail to reject the null hypothesis H0

This implies that we cannot confirm a difference from random guessing.

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22
Q

Why can we not conclude that the null hypothesis is correct?

A

Failing to reject H0 does not mean it is true

There may be an undetected difference due to sample size limitations.

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23
Q

What condition does a small sample size fail to meet in the context of hypothesis testing?

A

Success-failure condition of the central limit theorem

This condition is crucial for the validity of hypothesis testing.

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24
Q

What is the null hypothesis (H0) in hypothesis testing?

A

Represents the status quo

It is the hypothesis that we assume to be true until evidence suggests otherwise.

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25
What is the alternative hypothesis (HA) in hypothesis testing?
Represents the research question being tested ## Footnote It is what we are trying to find evidence for.
26
What do we conclude if there is strong evidence for the alternative hypothesis?
Reject the null hypothesis ## Footnote This indicates that we find statistically significant evidence in favor of the alternative.
27
What is the purpose of calculating the p-value in hypothesis testing?
Quantifying the strength of evidence against the null hypothesis ## Footnote The p-value helps determine whether the null hypothesis can be rejected.
28
What is a Type 1 Error in hypothesis testing?
False positive: rejecting H0 when it is actually true ## Footnote This error leads to incorrect conclusions about the presence of an effect.
29
What is a Type 2 Error in hypothesis testing?
False negative: failing to reject H0 when HA is true ## Footnote This error results in missing a true effect.
30
How can we reduce the Type 1 Error rate in courts?
Raise the standard for conviction ## Footnote This could lead to more Type 2 Errors as it becomes harder to convict the guilty.
31
What happens when we reduce the Type 2 Error rate?
We may increase the Type 1 Error rate ## Footnote This reflects the trade-off between false positives and false negatives.
32
What is the rule of thumb for rejecting the null hypothesis?
Do not reject H0 unless we have strong evidence ## Footnote Strong evidence typically means a low p-value.
33
What is the desired false positive rate in hypothesis testing?
5% ## Footnote This corresponds to a significance level (α) of 0.05.
34
What is the significance level in hypothesis testing?
The probability of incorrectly rejecting H0 ## Footnote It is denoted by α and is set based on the context of the test.
35
What does a 95% confidence interval indicate in hypothesis testing?
Type 1 Error occurs about 5% of the time ## Footnote This is when the sample's estimate is significantly different from the population parameter.
36
What does using a 99% confidence interval imply?
α = 0.01 ## Footnote More stringent criteria are used to avoid false positives.
37
What does using a 90% confidence interval imply?
α = 0.1 ## Footnote This is used when avoiding false negatives is prioritized.
38
What is the Central Limit Theorem?
Means from samples will be approximately normal in distribution as sample size increases ## Footnote This theorem underlies many statistical methods.
39
What is the relationship between sample proportions and population proportions?
Sample proportions will be nearly normally distributed with mean equal to the population proportion p ## Footnote This holds true as sample sizes become large.
40
What does the Central Limit Theorem state about the sampling distribution as sample size increases?
The sampling distribution gets more normally shaped ## Footnote This is a key concept in statistics.
41
What is the mean of sample proportions according to the Central Limit Theorem?
Mean equal to the population proportion, p
42
What is the standard error for sample proportions?
Standard error equal to the formula derived from the population proportion
43
What is the first condition of the Central Limit Theorem (CLT)?
Sampled observations must be independent
44
What is more likely to ensure independence in sampling?
Random sampling/assignment
45
What is the maximum sample size in relation to the population for the CLT to hold?
Sample size n must be LESS than 10% of the population
46
In the example provided, what was the sample size used to estimate pushback from the town?
n = 100 people
47
What happens to standard error as sample size increases?
Standard error decreases
48
What is the difference between p-value and effect size?
The p-value is different than the size of the effect
49
What does a small p-value indicate in hypothesis testing?
Strong evidence against the null hypothesis
50
What is the significance level (alpha) typically set at in hypothesis testing?
α = 0.05
51
What is the null hypothesis (H0) in the example regarding coal usage?
There is no majority support or opposition to expanding coal usage
52
What does statistically significant mean in the context of hypothesis testing?
The sample statistic is unusual enough relative to the null hypothesis to reject it
53
What two statements are evaluated in a hypothesis test?
Two mutually exclusive statements about a population
54
What is the success-failure condition in hypothesis testing?
Check if n*p and n*(1-p) are both greater than or equal to 10
55
How do you calculate the p-value in hypothesis testing?
By evaluating the tail area under the null distribution
56
What is the outcome if the p-value is less than the significance level?
Reject the null hypothesis
57
What does a good p-value not necessarily imply?
The results are useful and interesting
58
What is the null value used for in hypothesis testing?
The null value p0 is used for the proportion in calculations
59
What does the term 'unusual enough' refer to in hypothesis testing?
How far the sample statistic is from the null hypothesis value
60
What is the critical region in hypothesis testing?
The area in the tail of the distribution where we reject the null hypothesis
61
What does winning 65% of foosball games indicate about my skill level?
It suggests a proficiency in foosball, but further statistical analysis is needed to claim superiority with confidence.
62
Can I claim I'm better at foosball with 99% confidence if I win 65% of 80 games?
Statistical tests are required to determine if the claim is valid.
63
What are the hypotheses in the context of statistical testing?
Ho (null hypothesis) and Ha (alternative hypothesis).
64
What is the significance level in hypothesis testing?
It is the threshold at which you determine whether to reject the null hypothesis.
65
What is the p-value in hypothesis testing?
It indicates the probability of observing the data if the null hypothesis is true.
66
If a federal loan program benefits a community if at least 30% of businesses qualify, what action is taken if only 28% qualify from a sample of 100?
Oppose the federal loan program based on the sample results.
67
What was the outcome of the Pew Research Poll regarding payday loan regulations?
51% of 826 respondents supported increased regulation.
68
What does p ≠ 0.50 indicate in the context of the payday loan borrowers' support?
It suggests that the majority either support or oppose the regulation.
69
How is the standard error calculated in a one-proportion hypothesis test?
Using the null value, p0.
70
What does the Z-score represent in hypothesis testing?
It is the test statistic computed from the point estimate.
71
What is the significance of a p-value larger than 0.05?
It indicates weak evidence against the null hypothesis.
72
What does a high p-value suggest about the null hypothesis?
Your data are likely compatible with a true null hypothesis.
73
What is the relationship between p and p-hat?
Both are point estimates for a population proportion, but p-value is different.
74
What defines statistical significance in hypothesis testing?
When the sample statistic is unusual enough relative to the null hypothesis.
75
What are common alpha values used in hypothesis testing?
0.05 and 0.01.
76
Does alpha always equal 0.05?
No, it can be adjusted based on the application.
77
What should you consider when selecting a significance level?
The type of error you are more concerned about (false positives vs. false negatives).
78
What happens if a false positive is especially costly?
Choose a smaller significance level (e.g., α = 0.01).
79
What is a strategy to reduce the false negative rate?
Collect more data.
80
What is the null hypothesis in the context of flawed hinges rate?
H0: p = 0.002.
81
What is the alternative hypothesis regarding the rate of flawed hinges?
HA: p ≠ 0.002.
82
What is the significance level that seems reasonable for the flawed hinges example?
0.05.
83
What should the car company do if evidence suggests one supplier's parts are better?
Reject H0 and switch suppliers.
84
What might be an appropriate significance level for choosing a supplier based on safety?
α = 0.10.
85
What should a car company do when safety is involved and evidence is moderately strong?
Switch to the slightly more expensive manufacturer ## Footnote This decision is based on the rejection of the null hypothesis (H0)
86
What is a slightly larger significance level that might be appropriate in safety-related decisions?
α = 0.10
87
What is the significance level in hypothesis testing?
A threshold that determines how far out from the null hypothesis value we draw the line on the graph
88
What are the common alpha values based on tradition?
* 0.05 * 0.01
89
What must a researcher/analyst do regarding the significance level before conducting a test?
Select an alpha
90
What is considered bad form in hypothesis testing?
Raising the significance level after analysis to find statistical significance
91
What is the null hypothesis in the example regarding average energy cost?
The true population mean equals the hypothesized null mean (µ0 = 260)
92
What does the alternative hypothesis state in the energy cost example?
The true population mean differs from the hypothesized null mean (µ0 ≠ 260)
93
What is the critical region in statistics?
Shaded areas in a distribution where the sample mean falls under the null hypothesis
94
What does a sample mean falling within the critical region indicate?
It is statistically significant at the α=0.05 level
95
What does a P value represent?
The probability of obtaining an effect at least as extreme as the one in your sample data, assuming the truth of the null hypothesis
96
What happens when a P value is less than or equal to the significance level?
Reject the null hypothesis
97
What is the significance level that guards against false negatives?
α = 0.01
98
What is the outcome when a sample mean does not fall within the critical region at α=0.01?
Fail to reject the null hypothesis
99
What are the two types of errors in hypothesis testing?
* Type 1 Error: False positive * Type 2 Error: False negative
100
What is the standard error in hypothesis testing?
Calculated based on the sampling distribution
101
What is a test of group differences used for?
To determine if two groups' opinions or measurements differ in a larger population
102
What statistical tests are used for group differences?
* T-test (2 groups) * ANOVA (more than 2 groups)
103
What do tests of association/correlation examine?
The relationship between two numerical variables
104
What does the correlation coefficient R indicate?
The strength and direction of a linear relationship between two variables
105
What does R² represent in linear regression?
The proportion of variance for one variable that's explained by another variable
106
What does ANOVA stand for?
Analysis of Variance
107
What is the purpose of tests of association/correlation?
To determine the relationship between two numerical variables
108
What does a correlation coefficient R indicate?
The strength and direction of a linear relationship between two variables
109
What does R² represent in regression analysis?
The proportion of variance in the dependent variable that can be explained by the independent variable(s)
110
What is the main goal of regression analyses?
To predict the value of a dependent variable based on independent variable(s)
111
What is Ordinary Least Squares (OLS)?
A method for estimating the parameters in a linear regression model
112
What is the purpose of testing group differences?
To determine if two groups' measurements are significantly different in the larger population
113
Provide an example of a scenario where group differences might be tested.
Mental health outcome scores after new treatment
114
In the context of regression, what does the term 'dependent variable' refer to?
The outcome variable that researchers are trying to predict
115
What does the statement 'if they have eggs, get a dozen' illustrate in programming?
The importance of being explicit in instructions or commands
116
Fill in the blank: Regression analyses are powerful tools that allow analysts to ______ outcomes of future observations.
anticipate
117
What does CI95Zstar represent in statistical calculations?
The z-score for a 95% confidence interval
118
What is the formula for calculating standard error (SE) for a class vaccination guess?
sqrt(0.33*0.67/12)
119
True or False: The programmer returned home with 12 gallons of milk because of an implicit instruction.
True
120
What does SEnew represent in the context of standard error calculations?
The standard error for a new estimate
121
What statistical function is used to find the probability of a value in a normal distribution?
pnorm

BA 216 📊 (14 decks)

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