13. The MSU College of Education conducted a research project to determine if st

Question

13. The MSU College of Education conducted a research project to determine if stay-at-home mothers spend more time helping their children with school related work than did working mothers. A sample of 35 stay-at-home mothers (n1) and 24 working mothers (n2) were surveyed. The stay-at-home mothers spent an average of 235 minutes a week helping their children with a standard deviation of 32.5 minutes per week. Working mothers spent an average of 220 minutes a week helping their children with a standard deviation of 16.5 minutes per week. Is there any evidence that stay-at-home mothers spend more time helping their children than working mothers? Use alpha=.05.

(1) What is the correct alternative hypothesis for this test? H1: u1 = u2 H1: u1 > u2 H1: u1 < u2 H1: u1 - u2 < 0 H1: u1 - u2 = 5

(2) What is the correct statistical test to use? right tailed z-test two tailed t-test left tailed t-test right tailed t-test two tailed z-test

(3) What is the calculated value for this test? 1.30 1.67 -1.67 2.08 11.09

(4) What is the correct managerial decision? Working mothers spend more time helping their children than do stay-at-home mothers. Both types of mothers spend the same amount of time helping their children. Stay-at-home mothers spend more time helping their children than do working mothers. Accept the null hypothesis. Fathers need to spend more time helping the children of working mothers.

Explanation / Answer

(1) correct choice for alternative hypothesis is H1: u1 > u2

(2) correct choice for statistic test is right tailed t-test

here n1=35 and n2=24 we should use t-test as ( since n2<30, we should use t-test instead of z)

(3)correct choice is t=2.08

(4) here one-tailed p-value is less than alpha=0.05, so we fail to accept H0 and conclude that

Working mothers spend more time helping their children than do stay-at-home mothers.

following information has been generated

here we use t-test with null hypothesis H0:mean1=mean2 and alternate hypothesis H1:mean1 >mean2

t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2

sample mean s s2 n (n-1)s2 stat-at-home 235 32.5 1056.25 35 35912.5 working 220 16.5 272.25 24 6261.75 difference= 15 1328.5 59 42174.25 sp2= 739.8991228 sp= 27.20108679 t= 2.080743948 one tailed p-value= 0.020981089

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