Question

Your company purchases washers from supplier XYZ. It is important that the diameter of the whole be no more than 0.3 inch. If the whole is too large than your company will not be able to use the washer. If the whole is small, the washer can be re-worked. You decided to take a sample of 64 washers from supplier XYZ to check to be sure that the diameter doesn’t exceed 0.3 inch on the average. Sample results are as follows: Sample Average = .305 Sample Standard Deviation =.02 Use α = .10 to decide if to purchase washers from supplier XYZ or not.

Answer 1

Solution :

= 0.3

= 0.305

s = 0.02

n = 64

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0.3

H_a : > 0.3

Test statistic = t

= ( - ) / s / n

= (0.305 - 0.3) / 0.02 / 64

= 2

P(z >2 ) = 1 - P(z < 2 ) = 0.0249

P-value =

= 0.10

Since p =0.0249 < 0.10, it is concluded that the null hypothesis is rejected.

There is enough evidence to claim that the population mean μ is greater than 0.3