Question

A 90% confidence interval for u using the sample results X = 131.2, s=55 , and n= 50 Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places. Margin of error:? 90 Confidence Interval?

Answer 1

131.2 ;

12.8 ;

(118.4, 144)

Explanation:

Given :

X = 131.2, s=55 , and n= 50

Point estimate of the mean :

Since, sample size is large (n > 30) ; the sample mean = population mean according to the center limit theorem :

Margin of Error = Zcritical * s / sqrt(n)

Zcritical at 90% = 1.645

Margin of Error : 1.645 * (55 / sqrt(50))

Margin of Error : 1.645 * 7.7781745

Margin of Error = 12.795097

Margin of Error = 12.8

The confidence interval (C.I) :

C.I = x ± margin of error

C. I = 131.2 ± 12.8

(131.2 - 12.8) ; (131.2 + 12.8)

(118.4, 144)