Question

Length of Growing Seasons: The growing seasons for a random sample of 44 U.S. cities were recorded, yielding a sample mean of 188.6 days and the population standard deviation of 53.6 days. Estimate the true population mean of the growing season with 95% confidence. Round your answers to at least one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 188.6

Population standard deviation =    =53.6

Sample size n =44

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 53.6/ 44)

= 15.8
At 95% confidence interval estimate of the population mean
is,

- E < < + E

188.6 - 15.8 <   <188.6 + 15.8

(17.3 , 204.4)