Question

A researcher in interested in whether students who are musicians have higher intelligence test scores than students in the general population. The mean for the general population is 100. The researcher selects musicians from local high schools and gives them an intelligence test, with a mean of 105. SS 725 for the 2. 30 sample Null Hypothesis (Ho): μ State in words: Alternative Hypothesis (Ha): μ > State in words: df= t critical value (with α : .05): One-tailed or two-tailed test? Compute t obtained value: Reject or fail to reject the null hypothesis? Interpret result:

Answer 1

μ = 100, M = 105, n = 30, s^2 = 725/29 = 25, SE = s/√n = 5/√30 = 0.913

Ho: μ ≤ 100

Ho: Students who are musicians have the same or less score than the general students

Ha: μ > 1000

Ha: Students who are musicians have higher score than the general students

One-tailed test

Df = 29

Critical t- score = 1.6991

Test statistic t = (x-bar - μ)/SE = (105 - 100)/0.913 = 5.476

Since 5.476 > 1.6991, reject Ho

Conclusion: Students who are musicians have higher score than the general students