Katie Sr Yr stats sample problem 16

Problem 17: Study Method Comparison

A professor wants to know whether students who use flashcards perform better than those who use highlighting when preparing for exams.
Two independent samples of students were tested.
The table below shows their test scores out of 100:
Part 1: What type of test is appropriate for this scenario?

• Paired sample t-test

• 2-sample t-test (independent samples)

• 2-proportion z-test

• 1-sample t-test

Part 2: What are the correct null and alternative hypotheses?

• H0:μ1=μ2,H1:μ1≠μ2

• H0:μ1=μ2,H1:μ1>μ2

• H0:μ1>μ2,H1:μ1=μ2

• H0:μ1≠μ2,H1:μ1=μ2

Part 3: What are the sample means and standard deviations?

• xˉ1=90.5, s1=3.5; xˉ2=82.3, s2=2.7

• xˉ1=87.2, s1=2.3; xˉ2=79.6, s2=3.1

• xˉ1=89.25, s1=2.71; xˉ2=79.75, s2=2.43

• xˉ1=88.0, s1=3.8; xˉ2=80.0, s2=2.5

Part 4: What is the value of the test statistic?

• 6.91

• 4.13

• 7.42

• 5.25

Part 5: What is the approximate P-value?

• 0.004

• 0.0001

• < 0.0001

• 0.012

Part 6: What is the correct decision at α=0.05?

• Fail to reject H0

• Reject H0

• Increase the significance level

• Retest with a paired design

Part 7: What is the correct conclusion based on the hypothesis test?

• There is strong evidence that flashcard users score higher.

• There is not enough evidence that flashcards work.

• Highlighting is significantly better than flashcards.

• Both methods are equally effective.

Part 8: What is the 95% confidence interval for the difference in test scores (flashcards - highlighting)?

• (6.75, 12.25)

• (4.81, 13.2)

• (5.45, 11.3)

• (7.11, 12.89)