Answer to Question #199664 in Statistics and Probability for Chadddddddy

Question

Use the steps to solve the following problems

1. A politician engaged the services of a private opinion pollster to determine the sample size needed among his constituents to interview about their perceptions on the freedom of information bill. Previous polls revealed that

approximately 62.5% are in favor of the bill. The politician adopted the 0.95 level of confidence and off the population value by at most 0.02.

2. A transportation company wants to know the amount of time it takes a bus

to travel from one bus stop to the next. From past observations, the standard

deviation is 5 hours. How many measurements are needed in order to be 95% certain that

the maximum error of estimate will not exceed 1 hour? What sample size is required for a maximum error of 2 hours?

Answer 1

1.

Error:

$ME=Z_{0.95}\sqrt{\frac{p(1-p)}{n}}=1.96\sqrt{\frac{0.625(1-0.625)}{n}}\le0.02$

$n\ge\frac{1.96^2\cdot0.625\cdot0.375}{0.02^2}=2251$

2.

Error of estimate:

$SE=\sigma/\sqrt{n}=1$

$n=\sigma^2/SE^2=5^2=25$

$SE=2$

$n=5^2/2^2=25/4=7$