Question

A sample of 27 elements produced a mean of 124 and a standard deviation of 16. Assuming that the population has a normal distribution with unknown population standard deviation, the 98% confidence interval for the population mean is:

a. 115.50 and 132.50

b. 117.50 and 130.50

c. 114.25 and 133.75

d. 116.37 and 131.63

Answer 1

Solution :

Given that,

sample size = n = 27

Degrees of freedom = df = n - 1 = 27 - 1 = 26

t _/2,df = 2.479

Margin of error = E = t_/2,df * (s /n)

= 2.479 * (16 / 27)

= 7.63

The 98% confidence interval estimate of the population mean is,

- E < < + E

124 - 7.63 < < 124 + 7.63

116.37 < < 131.63

option d. is correct