Question

A simple random sample of size 39 has mean 3.64. The population standard deviation is 1.55. Construct a 95% confidence interval for the population mean.

1.The parameter is the population (choose one) mean, proportion, standard deviation, variance

2. The correct method to find the confidence interval is (choose one) z, t, chi square method

Answer 1

Solution :

Given that,

1) parameter = population mean

2) Point estimate = sample mean = = 3.64

Population standard deviation =    = 1.55

Sample size = n = 39

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

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

= 1.96 * ( 1.55 /  39)

= 0.49

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

  ± E

3.64 ± 0.49   

( 3.15, 4.13 )