Question

The mean number of hours of part-time work per week for a sample of 278 Metro State students is 20. If the margin of error for the population mean with a 95% confidence interval is 1.5, construct a 95% confidence interval for the mean number of hours of part-time work per week for Metro State University students. (4 points)

Lower Limit: ____________

Upper Limit: ____________

Answer #1

Solution :

Given that,

Point estimate = sample mean =
= 20

Sample size = n =278

margin of error E = 1.5

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2}
= Z_{0.025} = 1.96

At 95% confidence interval estimate of the population mean

is,

- E <
<
+ E

278- 1.5 <
< 278+ 1.5

276.5<
< 279.5

( lower limit = 276.5 upper limit= 279.5

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