Question

Cheap Texts, Inc. sells college textbooks online. The CEO of the company hears a rumor that μ, the mean price among all the books for sale at the website, is equal to $100. He suspects that the unknown mean is actually less than $100. To investigate, he uses a computer to take a random sample of 23 books. The same mean price is $97.93 and the population standard deviation is known to be σ = $10.80. Assume the population of book prices is normally distributed. Do you have significant evidence that the population mean price is less than $100? Report ?0, ??, the rejection region (use α = .025), test statistic, conclusion, and p-value.

Answer 1

To Test :-

H0 :- µ = 100
H1 :- µ < 100

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 97.93 - 100 ) / ( 10.8 / √( 23 ))
Z = -0.9192

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z(0.025) = 1.96
Z > -Z(α) = -0.9192 > -1.96
Result :- Fail to reject null hypothesis

P value = P ( Z < 0.9192 ) = 0.1790 ( From Z table )

There is insufficiet evidence to support the claim that  the population mean price is less than $100.