Question

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).

Answer 1

ANSWER::

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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