Question

9. (10 points) A researcher was interested in comparing the GPAs of male and female students at CofC. Two independent simple random samples of 49 females and 36 males Cof students resulted in the following summaries: Females: R1 = 3.25, s; = 0.26; Males: fz = 3.06,82 = 0.59. Is it reasonable to think that female CofC students have a higher mean GPA than male CofC students? a) State the null and altemative hypotheses symbolically. b) Check assumptions and choose an appropriate test procedure. c) Compute the value of the test statistic. d) Determine the P-value. Use df = 45. Please show your work. e) Based on the P-value, what is the degree of evidence against the null hypothesis? ) Interpret the results of the hypothesis test by using the degree of evidence against the null hypothesis.

Answer 1

Soln Suppose Hi and My be the population meam of GPAS of female and male students at cofc respectively. Here we have to test the hypothesis that Ho: M = My Us Hai Mi > M2 Since the samples are independent thus we use two sample t test. Notice that here there x's no x's no information about the equality of varina of popu dation. Thus we case Welch's t-test, whose test statistic x's given by X - X2 t = + S₂2 ni na 大二 3.25 -3.06 1.8076 こ (0.2672 (0.5912 49 36 Here df = u5, thus p-value is calculated as p-valu = P(tus » 1.8076) = Since 0.0387 p-value xs dess than 0.05, thus there is strong evidence against the Noll hyls.

reasnable to say that the female Gofc x} strong evidence against the Mull hypothesis, this it is ② Since there Students have a higher mean GPA tham male cofc students.