Question 1193959: Over the last several years, the use of cellphones has increased dramatically. An article in USA Today reported that according to a poll, the mean talking time per month for cellphones was 372 minutes for men and 275 for women, while the mean talking time per month for traditional home phones was 334 minutes for men and 510 minutes for women. Suppose that the poll was based on a sample of 100 men and 100 women, and that the standard deviation of the talking time per month for cellphones was 120 minutes for men and 100 minutes for women, while the standard deviation of the talking time per month for traditional home phone was 100 minutes for men and 150 minutes for women. (critical value = +1.96)
a. Is there evidence of a difference in the mean monthly talking time on cellphones for men and women?
b. Is there evidence of a difference in the mean talking time on traditional home phone for men and women?
2. Management training programs are often instituted to teach supervisory skills and thereby increase productivity. Suppose a university psychologist administers a set of examination to each of 10 graduating students before such training program begins and then administers similar examinations at the end of the program. Examinations are designed to measure supervisory skills, with highest scores indicating increased skills. The results are shown below:
Student Before Training After Training
1 63 78
2 93 92
3 84 91
4 72 80
5 65 69
6 72 85
7 91 99
8 84 82
9 71 81
10 80 87
Do the data provide evidence that the training program is effective in increasing supervisory skills, as measured by the examination scores? Use 0.10 significance level. (critical value = +1.383)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Here is 2.
Ho: change - or same
Ha: change +.
alpha=0.10 p{reject Ho|Ho true}
test stat is a t (paired t) df=9
t=(difference/sd/sqrt(10)
mean is 6.9 sd=5.43
test stat is 6.9/5.43/sqrt(10)=4.01 highly significant at the 0.10 level
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Home phone
Ho: mu men=mu women
Ha: not equal
alpha=0.05 p{reject Ho|Ho true}
test stat is a 2 sample t df=198 with C.V actually a little more than 1.96 but will use that value
t=(diff in means)/sqrt{(sigma 1^2/n1+sigma2^2/n2)}
pooled sd: {{ (n1-1)s1^2+(n2-1)s2^2/(n1+n2-2 }}=sqrt(99*10000+99*22500)=127.47 min pooled sd
so t=-176/127.47 sqrt(2/100)=-176/18.03=-9.76
This is highly significant at the 0.05 level p <<0.0001
Cell phone
difference in means is +97 (men-women)
pooled sd is sqrt (99*120^2+99*100^2)=110.45
and the denominator is 110.45*sqrt(.02)=15.62
the quotient is 6.21 and this is highly significant.
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