Question

Problem 1. The director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer’s specifications, which indicate that the cloth should have a mean breaking strength of 70 pounds and a standard deviation of 3.5 ponds. A sample of 49 pieces of cloth reveals a sample mean breaking strength of 69.1 pounds. Is there evidence that the machine is not meeting the manufacturer’s specifications for mean breaking strength?

Answer 1

Solution :

Given that

= 70

= 69.1

=3.5

n = 49

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 70

Ha :    70

Test statistic = z

= ( - ) / / n

= ( 69.1 - 70 ) / 3.5 / 49

= -1.8

The test statistic = -1.8

P-value = 2 * P ( Z < -1.8 )

= 2 * 0.0359

= 0.0718

P - value = 0.0718

= 0.05  

0.0718 > 0.0718

P-value >  

Fail to reject the null hypothesis .

There is insufficient evidence to claim