Question

The college bookstore tells prospective students that the average cost of its textbooks is $92 per book, with a standard deviation of $15. The engineering students think that the average cost of their books is higher than the average for all students.

To test the bookstore's claim against their alternative, the engineering students collect a random sample of size 45, and calculate xbar = $97:34. Conduct a hypothesis test with σ = 0:05 to see if the students' claim is supported. Use the classical approach.

Answer 1

Solution :

The null and alternative hypothesis is ,

H0 :   = 92

Ha : > 92

Test statistic (t) =

= ( - ) / s / n

= (97.34 - 92) / 15 / 45

Test statistic = 2.39

P-value = 0.0106

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to support the claim.