Question

Home loan approval

Suppose the time that it takes a certain large bank to approve a home loan is normally distributed with mean (in days) μ and standard deviation σ = 1. The bank advertises that it approves loans in 5 days, on average, but measurements on a random sample of 100 loan applications to this bank gave a mean approval time of 5.2 days. Is this evidence that the mean time to approval is actually more than advertised?

1) (4 points)Write down in both symbols and words the null hypothesis and alternative hypothesis that you want to test.

2) (6 points)What type of Significance Test should you use to test your hypothesis? Write down the Test Statistic formula, and calculate the value of the Test Statistic.

3) (4 points)Find the P-value.

4) (3 points)Suppose the level of significance you chose for your test is the conventional 0.05 (5%), explain what conclusion you can draw about the hypothesis.  

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


Z = 2

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

P value = P ( Z > 2 ) = 0.0228

Decision based on P value
P value = P ( Z > 2 ) = 0.0228
Reject null hypothesis if P value <    level of significance
P - value = 0.0228 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that the mean time to approval is actually more than advertised.