Question

A manufacturing process is designed to produce a part with an average length of 450 millimeters. A random sample of 20 parts has an average length of 443 millimeters and a standard deviation of 22 millimeters. Use a statistical test at a 0.05 level of significance to decide if the average part length is different from the designed one. State any assumptions you are making.

Answer 1

Solution :

The null and alternative hypothesis is ,

H0 :   = 450

Ha :    450

= 443

s = 22

n = 20

degrees of freedom = n - 1 = 20 - 1 = 19

Test statistic = t =

= ( - ) / s / n

= (443 - 450) / 22 / 20

Test statistic = t = -1.42

This is the two tailed test,

P( t < -1.42 )

= 0.0859

P-value = 2 * P( t < -1.42 )

P-value = 2 * 0.0859

P-value = 0.1718

= 0.05  

P-value >

Fail to reject the null hypothesis