For the 2006 GSS a comparison of females and males on the nu

For the 2006 GSS, a comparison of females and males on the number of hours a day that the subject watched TV gave:

Group                         N         Mean       Standard deviation

Females           1117    2.99           2.34

Males              870      2.86           2.22

a. Conduct all parts of a significance test to analyze whether the population means differ for females and males (at ?=.05). Report the conclusion.

b. Find the 95% confidence interval comparing the means for females and males. Can you conclude that the population means are different (without conducting the test in part a)?

Solution

H0: means are the same for males and females

Ha: Means are different.

Two tailed test

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z for 95% CI= 1.96
declare p larger than alpha=0.05 not significant.

mean1 eq: 2.99 (variance= 5.476) (se= 0.07)
mean2 eq: 2.86 (variance= 4.928) (se= 0.0753)

Probability that var1<var2
p=0.05065 (left: 0.9493; double: 0.1014)

Difference between means:
M1-M2=2.99-2.86=0.13
sd=4.4925; se=0.1028
95% CI of difference:
-0.0715 <0.13< 0.3315
t-difference: 1.265
df-t: 1909.5; p= 0.89692
(left p: 0.1031; two sided: 0.2062)

As two sided p value = 0.2062, p value >0.05

Hence accept null hypothesis.

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99% CI of difference:
-0.1348 <0.13< 0.3948