Question

It is claimed that the average cost of tuition and fees at a four-year public college is greater than $5500. The standard deviation of college tuitions is known to be $659, and the mean tuition and fees of a sample of 36 schools is computed to be $5900.

a. Is this a two-tailed, right-tailed, or left-tailed test?

b. What is H1?

c. What is the test value?

d. Verify or deny the claim with 90% certainty.

Answer 1

It is right-tailed test

H0 :- µ <= 5500
H1 :- µ > 5500

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 5900 - 5500 ) / ( 659 / √( 36 ))
Z = 3.6419

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.1) = 1.28
Z > Z(α) = 3.6419 > 1.28
Result :- Reject null hypothesis

Decision based on P value
Reject null hypothesis if P value < α = 0.1 level of significance
P value = P ( Z < 3.6419 )
P value = 0.0001
Since 0.0001 < 0.1 ,hence we reject null hypothesis
Result :- Reject null hypothesis

d. It has been verify that the claim with 90% certainty.