Question

research suggests that the pressure of being timed may interfere with performance on tests that involve mathematical problems. a fictional study was conducted with 30 sixth graders. first, the sixth graders were given a math test that contained 50 problems and were told that they had only one hour to complete it (timed condition). the same sixth graders were later given a math test that contained 50 problems and were told that they could have as much time, as needed, to complete the test (unlimited time condition). the total number of correct answers for each sixth grader was then calculated for each condition. then, for each student, the difference between the two scores (timed - untimed) was calculated. the researchers hypothesized that the sixth graders would get fewer correct answers when they took the test with a time limit than when they had unlimited time. if μ₁ and μ₂ represent the number of correct answers during the timed condition and the unlimited time condition, respectively, and let μ_d be the mean of the differences in the number of correct answers (timed - untimed) of all sixth graders. which of the following are the appropriate null and alternative hypotheses? a. h₀:μ_d = 0 h_a:μ_d > 0 b. h₀:μ_d = 0 h_a:μ_d < 0 c. h₀:μ_d < 0 h_a:μ_d = 0

Explanation:

• The null hypothesis \(H_0\) is a statement of no difference. Here, it assumes that the mean difference in correct answers (timed - untimed) is zero, so \(H_0:\mu_d = 0\).
• The alternative hypothesis \(H_a\) is based on the researchers' claim. They hypothesized that students get fewer correct answers in the timed condition. So, the difference (timed - untimed) will be negative, which means \(\mu_d<0\).

Answer:

B. \(H_0:\mu_d = 0\), \(H_a:\mu_d<0\)