Question

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 (17 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?

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.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 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.

Answer 1

a)

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 ≠ p2

b)

For Carl:

n1 = 70, x1 = 21

p̂1 = x1/n1 = 0.3

For Norm:

n2 = 80, x2 = 17

p̂2 = x2/n2 = 0.2125

c)

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (21+17)/(70+80) = 0.2533

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.3 - 0.2125)/√[0.2533*0.7467*(1/70+1/80)] = 1.23

p-value :

p-value = 2*(1-NORM.S.DIST(ABS(1.2293), 1)) = 0.2190

Decision:

p-value > α, Do not reject the null hypothesis

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.