The building specifications in a certain city require that t

The building specifications in a certain city require that the sewer pipe used in residential areas have a mean breaking strength of more than 2500 pounds per lineal foot. A manufacturer who would like to supply the city with sewer pipe has submitted a bid and provided the following additional information: An independent contractor randomly selected seven sections of the manufacturer’s pipe and tested each for breaking strength. The results (pounds per lineal foot) follow:

2610 2750 2420 2510 2540 2490 2680

Is there sufficient evidence to conclude that the manufacture’s sewer pipe meets the required specifications?

(THIS QUESTION IS WORTH 14 POINTS, BTW. NOT REALLY SURE HOW)

Solution

Ans: The average breaking strength of the sample is the mean of the breaking strength measures of the sample units = 2571 pounds per lineal foot.

H0: <=2500

H1: > 2500

Here t statistic= 2571-2500/ 106= 0.6698

Let the level of significance be 5%, df= 7-1= 6

Thus, from t tables we find that the critical region is z> 1.943

According to the above calculation, as the calculated t value is less than 1.943, we can conclude that the null hypothesis can not be rejected. Thus, the evidence supports that the manufacturers pipe do not meet the required specifications.