Question

Construct a 90​% confidence interval to estimate the population mean using the accompanying data. What assumptions need to be made to construct this​ interval?

x=59 σ=15 n=17

What assumptions need to be made to construct this​ interval?

A. The population is skewed to one side.

B. The sample size is less than 30.

C. The population must be normally distributed.

D. The population mean will be in the confidence interval.

With 90​% ​confidence, when n=17​, the population mean is between the lower limit of and the upper limit of .

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 59

Population standard deviation = = 15

Sample size = n = 17

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z_{0.05 = 1.645}

Z/2 = 1.645  
Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 15/ 17 )

= 5.98

At 90 % confidence interval estimate of the population mean is,

- E < < + E

59 - 5.98 <   < 59+ 5.98

53.02 <   < 64.98

( 53.02,64.98 )

Answer D. The population mean will be in the confidence interval.

With 90​% ​confidence, when n=17​, the population mean is between the lower limit of =53.02 and the upper limit of =64.98.