Question

Community CollegePresident claims that

1.On average, Community Collegestudents' GPA is more than 3.

2.The proportion of female students is about 50%.

3.Less than 20% of Community Collegestudents smoke.

4.On average, male and female have the same GPA.

5.On average, smokers are heavier (more weight) than non smokers.Useclass datato run thetests to confirm the president's claims.

Design Hypothesis, test statistic, and run both on p_value method and Critical Value method( 5 steps).(#4,and #5, runCV method)

Answer 1

1.Let m be population mean of community 'college students GVA, xm be sample mean , s be population standard deviation and n be sample size. Then

Ho: m=3, mean GVA is 3

H1: m>3, mean GVA is more than three, the claim of investiigator.

Then under Ho, the test statistic is z=(xm-m)/(s/n) follows Standard normal distribution. According to cv method, if zcal > ztabulated at alpha level of significance then Ho is rejected. According to p value method, if p value obtained is less than alpha level of significance then Ho is rejected where p value =Probability (z>zalpha) .This is one tailed test for right tailed.

4.Let m1 and m2 be average GVA for men and women in population, x1m and x2m be sample mean of GVA, n1 and n2 sample size, s be population standard deviation (assuming to be same), then

Ho:m1=m1, there is no change in mean GVA of men and women

H1:m1 not equal to m2, there is effect of gender on mean GVA or they don't have same average GVA.

Under Ho, the test statistic is (when s is known)

Z=(x1m-x2m)/s/(((1/n1)+(1/n2))^0.5) follows standard normal distribution, this is z calculated named as zcal. Obtain z tabulated from z table named as z tab, so according to cv method, if modulus zcal> modulus ztab at alpha level of significance the reject Ho. This is two tailed test.

5.Let m1 and m2 be average weight of smokers and non smokers in population, let x1m and x2m be sample mean weights of smokers and non smokers, let n1 and n2 be sample sizes, let s be population standard deviation (assuming it is known). Then

Ho: m1=m2, that is there is no effect of smoking habbit in mean weight of person.

H1:m1>m2, the smokers are heavier than non smokers.

Then, under Ho, the test statistics is

Z=(x1m-x2m)/s/((1/n1 +1/n2)^0.5) follows standard normal distribution, this is named z cal , obtain z tab from z table, if zcal> ztab at alpha level of significance reject Ho and we can conclude that president 's claim is true. This is right tailed test.

Thank you and please rate the answer.