Question

Suppose that a random sample of 13 adults has a mean score of 64 on a standardized personality test, with a standard deviation of 4. (A higher score indicates a more personable participant.) If we assume that scores on this test are normally distributed, find a 95% confidence interval for the mean score of all takers of this test. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) What is the lower limit of the confidence interval? What is the upper limit of the confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 64

Population standard deviation =    = 4

Sample size = n = 13

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 = 0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

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

= 1.96 * ( 4 /  13 )

= 2.2

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

  ± E

64 ± 2.2   

( 61.8, 66.2 )  

lower limit = 61.8

upper limit = 66.2