Question

# The college bookstore tells prospective students that the average cost of its textbooks for one quarter...

The college bookstore tells prospective students that the average cost of its textbooks for one quarter is \$180 with a population standard deviation of \$22.50. A group of smart statistics students thinks that the average cost is higher. In order to test the bookstore’s claim against their alternative, the students will select a random sample of size 35. Assume that the mean from their random sample is \$185.25. Perform a hypothesis test with α = 0.05 and state your conclusion. (Show all steps please)

a) State the null and alternative hypothesis (H0 and Ha). H0: Ha:

b) What is the test statistic for this sample (use at least 3 decimal places)?

c) What is the p-value for this sample? (use Statcrunch)

d)Evaluate the strength of the evidence and state the conclusion (in the context of this question).

Part a)

H0 :- µ = 180
H1 :- µ > 180

Part b)

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 185.25 - 180 ) / ( 22.5 / √( 35 ))
Z = 1.3804

Part c)

P value = P ( Z < 1.3804 )

= 0.0837

part d)

Reject null hypothesis if P value < α = 0.05 level of significance
Since 0.0837 > 0.05 ,hence we reject null hypothesis
Result :- We fail to reject null hypothesis

There is insufficient evidnece to support the claim that average cost is higher.

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