Question

(Refer to HW6 #2) Rural and urban students are to be compared on the basis of their scores on a
nationwide musical aptitude test. Two random sample of sizes 90 and 100 are selected from rural
and urban seventh grade students. The summary statistics from the test scores are
Rural Urban
Sample size 90 100
Mean 76.4 81.2
Standard deviation 8.2 7.6
Do these data provide strong evidence that there is a difference in population mean scores between
urban and rural students? Perform the hypothesis testing (at the significance level α = .01) by
answering the questions arranged in the following.
(a) Define the µ1 and µ2 in the context of the problem.
(b) Formulate the null and alternative hypotheses.
(c) State the test statistic and its distribution.
(d) Determine the critical value for α = .01 and state the decision rule.
(e) Calculate the observed value of the test statistic from the data.
(f) State whether H0 is rejected and tell why.
(g) Calculate the P-value and do the hypothesis testing based on the P-value.

Answer 1