Question

 

In a random sample of 29 residents of the state of Montana, the mean waste recycled per person per day was 1.0 pounds with a standard deviation of 0.57 pounds. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

 

Point estimate = sample mean = = 1.0

Population standard deviation = =0.57

Sample size = n = 29

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

Margin of error = E = Z_/2* ( /n)

= 1.96  * ( 0.57 / 29 )

= 0.207

At 99% confidence interval estimate of the population mean is,

- E < < + E

1.0 - 0.207 < < 1.0 + 0.207

0.793   < < 1.207)  

( 0.793, 1.207 )