Question

A simple random sample of size 44 has mean 3.01. The population standard deviation is 1.51. Construct a 90% confidence interval for the population mean.

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

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

Answer 1

Solution :

Given that,

1) The parameter is the population mean

2) Point estimate = sample mean = = 3.01

Population standard deviation =    = 1.51

Sample size = n = 44

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * ( 1.51 / 44 )

= 0.37

At 90% confidence interval estimate of the population mean is,

  ± E

3.01 ± 0.37   

( 2.64, 3.38 )