Question 998759: 8.32 In a survey of 2,395 adults, 1,916 reported that
e-mails are easy to misinterpret, but only 1,269 reported that
telephone conversations are easy to misinterpret. (Data
extracted from “Open to Misinterpretation,” USA Today,
July 17, 2007, p. 1D.)
a. Construct a 95% confidence interval estimate for the
population proportion of adults who report that e-mails
are easy to misinterpret.
b. Construct a 95% confidence interval estimate for the
population proportion of adults who report that telephone
conversations are easy to misinterpret.
c. Compare the results of (a) and (b).
8.40 If a quality control manager wants to estimate, with
95% confidence, the mean life of light bulbs to within +- 20 hours and also assumes that the population standard
deviation is 100 hours, how many light bulbs need to be
selected?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The proportion in the sample was 0.8
The SE is sqrt ((0.8)(0.2/2395}=0.00817
a 95% CI is 1.96*SE for the interval half width.
It equals 0.016
The CI is (0.784,0.816)
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Telephone
0.5298 is point estimate proportion
SE={0.5298*0.4702/2395}^(1/2)=0.0102
1.96*SE=0.02
The CI is (0.51,0.53). More decimal places may be added if desired. The CI is wider, because the proportion is closer to 0.5
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sample size unknown
we know that 1.96 * SE is the interval, and the interval must be +/- 20 hours
The SE is the SD/sqrt(n)
1.96*SD/sqrt(n)=20
square both sides
3.84*10000/n =400
n=38416/400=96.04 round to 97
Check this
mean +/- s/sqrt(n)
that is 100/sqrt(97)=10.153
That *1.96=19.90, slightly below 20 because need to round the 96.04 up to next higher.
97 light bulbs.
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