Carl Allen and Norm Nixon are two loan officers at a certain bank. The bank manager is interested in comparing the defau

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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 (21 of which defaulted) and 80 loans
approved by Norm (19 of which defaulted).
(a)
State the hypothesis test that the default rates are the same
for the two loan officers. (Let p1 =
the population proportion of Carl's loans that default, and
let p2 = the population proportion of
Norm's loans that default. Enter != for ≠ as needed.)
H0:
Ha:
(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. (Use
p1 − p2.
Round your answer to two decimal places.)
What is the p-value? (Round your answer to four
decimal places.)
p-value =
What is your conclusion?
Do not reject H0. We cannot conclude
there is a significant difference between the population default
proportions in the loans approved by Carl and the loans approved by
Norm.Reject H0. We cannot conclude there
is a significant difference between the population default
proportions in the loans approved by Carl and the loans approved by
Norm. Reject H0. We
can conclude there is a significant difference between the
population default proportions in the loans approved by Carl and
the loans approved by Norm.Do not
reject H0. We can conclude there is a
significant difference between the population default proportions
in the loans approved by Carl and the loans approved by Norm.