AP Stats two-sample t test conditions practice questions
This study set contains practice questions for AP Statistics focusing on the conditions necessary for conducting two-sample t tests. Perfect for preparing for the AP exam with real-world examples.
Quiz(28 questions)
1. What assumption must be checked regarding the distributions of the samples when conducting a two-sample t-test?
Terms in this Study Set(28)
Two-Sample t-Test Conditions(16)
What assumption is required for normality?
Both sample distributions should be approximately normally distributed, especially if sample sizes are small.
True or False: Sample sizes must be equal for a two-sample t-test.
False. Sample sizes can vary, but both should be sufficiently large or normal.
Fill in the blank: The two-sample t-test assumes that the two samples are __________.
independent from each other.
What condition must be met regarding variance?
The variances of the two populations should be approximately equal (homogeneity of variance).
When is a two-sample t-test appropriate?
When comparing means from two independent groups, like test scores of students from two different schools.
Example scenario: Is a two-sample t-test valid?
Comparing earnings of male and female employees in a company. - Independent samples - Sufficient sample size - Normal distributions.
True or False: Outliers can significantly affect t-test results.
True. Outliers can skew results and violate normality assumptions.
What is the implication of unequal variances?
Use Welch's t-test, which adjusts for unequal variances in the two samples.
Cause → Effect: What happens if samples are not independent?
The results of the t-test become invalid, leading to incorrect conclusions.
Define 'independent samples.'
Samples where the selection of one does not influence the selection of the other.
When can we use the t-test for large samples?
If sample sizes are greater than 30, normality assumptions are less critical due to the Central Limit Theorem.
Example: Compare two brands of milk.
Brands A and B are tested for fat content. - Independent samples - Normal distribution assumed for each.
What is 'homogeneity of variance'?
The condition where the variances of the two populations being compared are equal or similar.
True or False: Non-normal data can be used if sample sizes are small.
False. Non-normal data with small samples violates assumptions of the t-test.
What to check before performing a t-test?
1. Normality of data 2. Independence of samples 3. Equality of variances.
Fill in the blank: The t-test can compare __________ between two groups.
mean values of a quantitative variable.
Application of Two-Sample t-Test(12)
Scenario: Two gyms compare average weights.
Gym A: 150 lbs, Gym B: 160 lbs. Use a two-sample t-test to determine if the difference is significant.
When to use a two-sample t-test?
When comparing means from two independent groups, e.g., test scores from two different schools.
True or False: Two-sample t-tests require equal sample sizes.
False. They can handle unequal sample sizes.
Fill in the blank: A two-sample t-test can help assess differences in ____ between groups.
means.
Interpretation question: A p-value of 0.03 was found.
There is significant evidence to reject the null hypothesis at the 0.05 level.
Comparing means of men vs. women salaries.
Men: 55,000. T-test results indicate a significant difference.
Scenario: Testing two teaching methods' effectiveness.
Method A: 85% pass rate, Method B: 78%. Conduct a two-sample t-test to compare effectiveness.
True or False: Two-sample t-tests assume normal distribution.
True. Both groups must be normally distributed, especially with small samples.
What does a confidence interval tell us?
The range in which the true difference between group means likely falls.
Example: Average monthly rent comparison.
Apartment A: 2,000. Analyze with two-sample t-test for significance.
Define: Independent samples.
Samples collected from different populations, e.g., students from two different colleges.
Cause and effect: Larger sample sizes lead to ____ in t-test results.
more reliable estimates.
Questions in this Study Set(28)
1. What assumption must be checked regarding the distributions of the samples when conducting a two-sample t-test?
2. What is the primary assumption of the two-sample t-test regarding the populations being compared?
3. True or False: The two samples in a two-sample t-test must be from the same population.
4. In a study comparing test scores from two different classes, Class A has an average score of 76 and Class B has an average score of 82. Which scenario requires a two-sample t-test?
5. Fill in the blank: A two-sample t-test assumes that the samples have __________ variances.
6. True or False: A two-sample t-test can only be used when both groups have a sample size greater than 30.
7. In which scenario is a two-sample t-test most appropriate?
8. Fill in the blank: The two-sample t-test can help determine if there is a statistically significant difference in the ____ of two groups.
9. Is the following scenario valid for a two-sample t-test? Comparing the average salaries of engineers and scientists at a company.
10. A researcher wants to analyze the average daily spending of two grocery stores. Store A reports an average of 90. If the t-test shows a p-value of 0.04, what does this indicate?
11. True or False: Outliers can impact the results of a two-sample t-test.
12. When applying a two-sample t-test to analyze the difference in the average time taken to commute to work for two groups, which of the following is NOT a necessary condition?
13. What should be done if the variances of the two samples are significantly different?
14. If a two-sample t-test results in a confidence interval of (1.5, 4.5), what does this imply about the difference between group means?
15. Cause → Effect: What happens if the samples in a two-sample t-test are dependent?
16. In a comparison of the average salaries of two different job positions, Position A earns 80,000 with a t-test resulting in a p-value of 0.10. What can we conclude?
17. What is the definition of 'independent samples' in the context of a two-sample t-test?
18. Which of the following scenarios is best suited for a two-sample t-test?
19. When can you use the t-test for large samples?
20. If a researcher obtains a larger sample size for one of the groups in a two-sample t-test, what effect does this have on the test results?
21. Consider two brands of yogurt compared for sugar content. This test is valid if:
22. In an analysis comparing average daily sales of two different stores, Store X has an average of 550 with a t-test showing a statistically significant result. What does this tell us?
23. What does 'homogeneity of variance' refer to?
24. Which of the following scenarios would NOT be appropriate for conducting a two-sample t-test?
25. True or False: Non-normal data can still be used for a two-sample t-test if the sample sizes are large.
26. What are the key conditions to check before performing a two-sample t-test?
27. Fill in the blank: The t-test can compare __________ between two groups.
28. Which of the following is NOT a condition that must be satisfied before conducting a two-sample t-test?
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