A researcher wants to test if the mean GPAs of all male and allfemale college st

Question

A researcher wants to test if the mean GPAs of all male and allfemale college students who actively participate in sports aredifferent. She took a random sample of 28 male students and 24female students who are actively involved in sports. She found themean GPAs of the two groups to be 2.62 and 2.74, respectively, withthe corresponding standard deviations equal to 0.43 and 0.38.

a. Test at the 5% significance level whether the mean GPAs of thetwo populations are different.

b. Construct a 90% confidence interval for the difference betweenthe two population means.

Explanation / Answer

Male: n1=28, xbar1=2.62, s1=0.43 Female: n2=24, xbar2=2.74, s2=0.38 =0.05, Z(0.025)=1.96 (check normal table) (a) The test hypothesis is Ho: 1=2 Ha: 1 not equal 2 The test statistic is Z=(xbar1-xbar2)/(s1^2/n1 + s2^2/n2) =(2.62-2.74)/sqrt(0.43^2/28 + 0.38^2/24) =-1.07 Since Z=-1.07>-1.96, we do not reject Ho. So we can not concludethat the mean GPAs of the two populations are different. (b) Given =0.1, Z(0.05)=1.645 (check normal table) The 90% CI is (xbar1-xbar2) ± Z*(s1^2/n1 + s2^2/n2) --> (2.62-2.74)± 1.645* sqrt(0.43^2/28 + 0.38^2/24) --> (-0.3047, 0.0647)

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