Question

In: Statistics and Probability

An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation...

An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation of 8. A psychologist gave the self-esteem test to a random sample of 60 individuals, and their mean score was 66. Construct a 95% confidence interval for the true mean of all test scores. 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

95%

confidence interval?
What is the upper limit of the

95%

confidence interval?

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 66

Population standard deviation =    = 8

Sample size = n = 60

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 * ( 8 /  60 )

= 2.024

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

- E < < + E

66 - 2.024 <   < 66 + 2.024

63.976 <   < 68.024

( 64.0 , 68.0 )

The Lower limit of the 95% confidence interval = 64.0

The Upper limit of the 95% confidence interval = 68.0


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