Question

Let x be a normal distribution with sigma equals 8 . A random sample size of 16 has sample mean 50.

a) Construct the 90% confidence interval for the population mean mu.

b)interpret the confidence interval computed in an above.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 50

Population standard deviation = =8

Sample size = n = 16

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (8 / 16 )

= 3.29

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

- E < < + E

50 - 3.29 <   < 50+ 3.29

46.71 <   < 53.29

( 46.71 ,53.29 )

The 90% confidence interval for the population mean mu IS =( 46.71 ,53.29 )