Carl Allen and Norm Nixon are two loan officers at a certain bank. The bank manager is interested in comparing the default rate on the loans approved by Carl to the default rate on the loans approved by Norm. In the sample of loans collected, there are 70 loans approved by Carl (14of which defaulted) and 80 loans approved by Norm (11of which defaulted).

(a)

State the hypothesis test that the default rates are the same for the two loan officers. (Letp₁= the population proportion of Carl's loans that default, and letp₂= the population proportion of Norm's loans that default. Enter != foras needed.)

H₀:

H_a:

(b)

What is the sample default proportion for Carl?

What is the sample default proportion for Norm?

(c)

Use a 0.05 level of significance.

Calculate the test statistic. (Usep₁p₂.

Round your answer to two decimal places.)

What is thep-value? (Round your answer to four decimal places.)

p-value =