Question

Find the confidence interval for the given values of ?, ?, ?⎯⎯⎯, and confidence level.

?=21, ?=42, ?⎯⎯⎯=53, confidence = 0.89

Enter your answer by filling in the blanks ( ____ , ____ ). Round final answers to 2 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 53

Population standard deviation =    = 21

Sample size = n = 42

At 89% confidence level

= 1 - 89%  

= 1 - 0.89 = 0.11

/2 = 0.055

Z/2 = Z_{0.055 = 1.598}

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

= 1.598 * ( 21 /  42 )

= 5.18

At 89% confidence interval estimate of the population mean is,

- E < < + E

53 - 5.18 <   < 53 + 5.18

47.82 <   < 58.18

( 47.82 , 58.18 )

The 89% confidence interval estimate of the population mean is : ( 47.82 , 58.18 )