10 A professor claims that there is a difference in the vari

10. A professor claims that there is a difference in the variability in final exam scores in calculus between students who are not math majors from those that are math majors. She believes that there is less variability with exam scores of math majors than non-math majors and hopes this test proves that belief. A random sample of ten students (non-majors) and a similar sample of ten students (math majors) from the professor’s freshman class roster were taken. Below is the data: (10 pts)
sample variance (non majors): 210.2 sample variance (majors): 36.5 confidence level: 95%
a. What is an appropriate null hypothesis that expresses the professor’s belief? b. What is an appropriate alternate hypothesis?
c. What is the value of the test statistic? d. What is the value of the critical value? e. What is the p value? f. What is your conclusion about the null hypothesis at a 95% confidence level? Reject / Not Reject? g. Using the Critical Value Test (test statistic vs. critical value), explain your conclusion concerning the null hypothesis? h. Using the p value test (p value vs. value), explain your conclusion concerning the null hypothesis? i. Would it be appropriate to use the “pooled-variance t test for testing the difference in means? Yes / No? Explain your answer.

Solution

n1=10,n2=10,s1²=210.2,s2²=36.5

answer of part (a) the null hypothisis is Ho:s1²=s2^{2 ,}

i.e. there is no difference in the variability in final exam scores in calculus between students who are not math majors from those that are math majors

answer of part (b)

the alternate hypothisis is HA:s1² not equal to s2^{2 ,}

i.e. there is difference in the variability in final exam scores in calculus between students who are not math majors from those that are math majors

answer of part (c)

here we go for F-test

F=s1²/s2² = 210.2/36.5=5.75

answer of part (c)

critical value =3,1788

answer of part (d)

critical value =3,1788

answer of part (e)

p value=0.00779

answer of part (f)

Reject null hypothesis

answer of part (g)

the calculated F value is more than critical value so we reject null hypothesis

answer of part (g)

since p value is less than alpha value , we reject null hypothiseis

answer of part (i)

NO, here we have to test of variability not difference of means