Question

A certain type of yarn is manufactured under specifications that the mean    tensile strength must be 22 psi. A random sample of 26 units out of a population of 60 units yields a mean tensile strength of 20 psi and a standard deviation of 4.8 psi.

Can we conclude from the data that the true mean tensile strength is less than 22 psi? If the random sample of 26 units were collected from a large population  with  the same mean and standard deviation, will your conclusion of part (i)  change?  Show by calculations.For both cases use, alpha=0.05

Answer 1

Solution :

= 22

=20

S =4.8

n = 26

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 22

Ha : < 22

Test statistic = t

= ( - ) / S / n

= (20 -22) / 4.8 / 26

= -2.124

Test statistic = t =  -2.124

P-value =0.0219

= 0.05  

P-value <

0.0219 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that