Final Exam Statistics

What is the primary purpose of a single-sample t-test?

• To compare the means of two independent groups.

• To compare the means of two dependent groups.

• To determine if a sample mean differs significantly from a known population mean.

• To analyze the variance within a single sample.

A researcher conducts a single-sample t-test and obtains a p-value of 0.03. What does this p-value indicate?

• There is strong evidence to reject the null hypothesis.

• There is weak evidence to reject the null hypothesis.

• There is strong evidence to fail to reject the null hypothesis.

• The test is inconclusive.

A psychologist wants to test if the average IQ of a sample of 25 students (mean IQ = 110, standard deviation = 10) differs significantly from the known population mean IQ of 100. Which of the following correctly represents the null hypothesis (H₀) for this single-sample t-test?

• μ ≠ 100

• μ = 110

• μ = 100

• μ ≠ 110

A researcher performs a single-sample t-test and finds a statistically significant result (p < 0.05). However, the effect size is very small. What should the researcher conclude?

• The results are highly meaningful and support the research hypothesis.

• The results are not meaningful despite statistical significance due to the small effect size.

• The results are inconclusive because the p-value is less than 0.05.

• The test was incorrectly performed.

A study uses a single-sample t-test to compare the average weight loss of participants in a weight-loss program to a hypothesized average weight loss of 10 pounds. The study finds a statistically significant difference (p < 0.01). However, the sample size was only 5 participants. What is the most appropriate evaluation of this study's findings?

• The results are highly reliable and generalizable to a larger population.

• The small sample size limits the reliability and generalizability of the results, despite statistical significance.

• The p-value is so low that the sample size is irrelevant.

• The study is perfectly valid and conclusive.

A researcher wants to investigate if a new teaching method improves student performance on a standardized test. The population mean score on the test is 75. The researcher collects data from a sample of students taught using the new method. Which of the following best describes the appropriate statistical test and the null hypothesis?

• Independent samples t-test; H₀: μ₁ = μ₂

• Paired samples t-test; H₀: μd = 0

• Single-sample t-test; H₀: μ = 75

• ANOVA; H₀: μ₁ = μ₂ = μ₃

A researcher uses a dependent samples t-test and finds a p-value of 0.02. Assuming a significance level of α = 0.05, what is the appropriate conclusion?

• Fail to reject the null hypothesis.

• Reject the null hypothesis.

• The test is inconclusive.

• The effect size is small.

A study measures participants' anxiety levels before and after a relaxation technique. The data are paired (before and after scores for each participant). What is the appropriate statistical test to determine if the relaxation technique significantly reduced anxiety?

• ndependent samples t-test

• Single-sample t-test

• Dependent samples t-test

• ANOVA

A researcher conducts a dependent samples t-test and finds a statistically significant difference (p < 0.01). However, the effect size is small (e.g., Cohen's d = 0.2). What is the best interpretation of these results?

• The results are highly meaningful and practically significant.

• The results are statistically significant but may not be practically meaningful due to the small effect size.

• The small effect size invalidates the statistical significance.

• The test was incorrectly performed.

Two studies investigate the effectiveness of a new sleep aid. Both use dependent samples t-tests. Study A has a larger sample size and a smaller p-value than Study B. Which study provides stronger evidence for the effectiveness of the sleep aid?

• Study B

• Study A

• Both studies provide equally strong evidence.

• More information is needed to compare the studies.