1. Marge N. O\'Vera\'s polling firm has been retained to estimate the mean time

ID: 3065034 • Letter: 1

Question

1. Marge N. O'Vera's polling firm has been retained to estimate the mean time to retirement, in years, of current state workers in California. (a) If Marge sampled 100 individuals and the mean and standard deviation of their answers were found to be 15 and 5 years, respec- tively, what would her 95% confidence interval for look like? (b) If a 95% confidence interval is required with a margin of error of E = .5 years, how large a sample would be needed to guarantee this level of precision? Use the sample standard deviation from part (a) as an estimate of .

Explanation / Answer

Result:

a).

CI = mean ± t* s/sqrt{n}

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

Sample Mean

Sample Size

100

Confidence Level

95%

Intermediate Calculations

Standard Error of the Mean

0.5

Degrees of Freedom

t Value

1.9842

Interval Half Width

0.9921

Confidence Interval

Interval Lower Limit

14.0079

Interval Upper Limit

15.9921

95% CI = (14.0079, 15.9921)

b).

Sample size for single mean

For 95%, z=1.96

d=0.5

sd=5

Sample size = (z2*s2)/d2

= (1.962*52)/0.52

=384.16

The sample size required= 385