Question

The lengths of steel rods produced by a shearing process are normally distributed. A random sample of 10 rods is selected; the sample mean length is 119.05 inches; and the sample standard deviation is 0.10 inch. The 90% confidence interval for the population mean rod length is __________.

Select one:

A. 118.99 to 119.11

B. 118.57 to 119.23

C. 119.00 to 119.30

D. 118.89 to 119.51

Answer 1

Solution :

Given that,

sample size = n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

t _/2,df = 1.833

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

= 1.833 * (0.10 / 10)

Margin of error = E = 0.06

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

- E < < + E

119.05 - 0.06 < < 119.05 + 0.06

118.99 < < 119.11

The 90% confidence interval for the population mean rod length is (118.99 to 119.11)

option A is correct