Question

In a metal fabrication​ process, metal rods are produced to a specified target length of 15 feet​ (ft). Suppose that the lengths are normally distributed. A quality control specialist collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and a standard deviation of 0.65 feet. The​ 95% confidence interval for the true mean length of rods produced by this process is​ _______.

A.

14.454 to 15.146 ft

B.

14.345 to 15.255 ft

C.

13.912 to 15.688 ft

D.

13.834 to 15.766 ft

E.

14.544 to 15.056 ft

Answer 1

solution

Given that,

= 14.8

s =0.65

n = 16

Degrees of freedom = df = n - 1 = 16- 1 = 15

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,15 = 2.131    ( using student t table)

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

=2.131 * (0.65 / 16) = 0.346

The 95% confidence interval estimate of the population mean is,

- E < < + E

14.8- 0.346 < < 14.8 + 0.346

14.454< < 15.146

( 14.454,15.146 )