Exhibit 10.6.A university wants to compare out-of-state applicants' mean SAT math scores (μ₁)to instate applicants' mean SAT math scores (μ₂).The university looks at 35 instate applicants and 35 out-of-state applicants.The mean SAT math score for instate applicants was 540,with a standard deviation of 20.The mean SAT math score for out-of-state applicants was 555,with a standard deviation of 25.It is reasonable to assume the corresponding population standard deviations are equal. Refer to Exhibit 10.6.At the 5% significance level,can the university conclude that the mean SAT math score for instate students and out-of-state students differ? A)No,because the confidence interval contains zero. B)Yes,because the confidence interval contains zero. C)No,because the confidence interval does not contain zero. D)Yes,because the confidence interval does not contain zero.

Question

Quizplus · Accepted Answer

We will conduct a two-sample t-test for the difference in means with equal variances. Using a significance level of 5%, the critical t-value with 68 degrees of freedom (n1 + n2 - 2 = 68) is 2.002. The calculated t-value is (555 - 540) / sqrt[(25^2 / 35) + (20^2 / 35)] = 2.68. Since the calculated t-value exceeds the critical t-value, we reject the null hypothesis that the means are equal and conclude that the mean SAT math scores for in-state and out-of-state applicants differ. The confidence interval also does not contain zero, which supports our conclusion.