Question

Question 1

A university claims that the average cost of books per student, per semester is $300. A group of students believes that the actual mean is higher than this. They take a random sample of 100 students and calculate the sample mean to be $345 with a standard deviation of $200.

a)         Perform a z-test to see if the students are correct, that the true mean is greater than $300 using α = 0.05. Specify the hypotheses, test statistic, decision rule and conclusion.

b) Calculate the p-value for the test in part a). Does this agree with your answer to part a)? Explain why or why not.

c)   Calculate a 90% confidence interval for µ. Does this agree with your answer to part a)? Explain why or why not.

Answer 1

To Test :-

H0 :-  

H1 :-

Test Statistic :-


Z = 2.25

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Conclusion :- There is sufficient evidence to support the claim that   the actual mean is higher than  $300.

Part b)

P value = P ( Z > 2.25 ) = 1 - P ( Z < 2.25 ) = 0.0122

Decision based on P value

Reject null hypothesis, if P value < level of significance

P value = 0.0122

0.0122 < 0.05, hence we reject null hypothesis

Part c)

Confidence Interval :-



Lower Limit =
Lower Limit = 312.1029
Upper Limit =
Upper Limit = 377.8971
90% Confidence interval is ( 312.1029 , 377.8971 )

Since does not lies in the interval  ( 312.1029 , 377.8971 ) , we can conclude that we reject null hypothesis.