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.)
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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
* ( 
/
= 1.96 * ( 8 /
= 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
orchestra answered 1 year agoRelated Solutions
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