Question

4. Consumers with credit scores below 600 have a very difficult time getting approved for mortgage loans. Last year 30% of Canadians had a credit score below 600. Due to the recent financial crisis, the Government of Canada is concerned that this proportion has increased. To investigate this, a simple random sample of 400 Canadians was selected for this study, and 140 people had credit scores less than 600. Use α = 0.05.

a) State the null and alternative hypotheses in the context of the question.

b) Calculate the value of the test statistic. Check the required condition(s) to validate the test statistic.

c) Find the p-value.

d) What conclusion can we draw?

Answer 1

Solution: Green, p=30.4 -0.30 n-40o X= 140 id=0.05 À -0.35 UOO a) rest hypothesis: <e yo Ho! P=0.30 Hai p 70.30 u b) Test Statistic Z p-P - / 0.35-0030 P(1-P) 0-30(1-0-30) = 2.1821 400 Z=2.1821 c) P-value =ooolus Using Z-table, rigut tail & Since , P-value is less than 0.05. Reject Ho, we have we have sufficient Evidence to support the claim.