Question

A large bank claims that approximately 14% of all house loans it issues are in default. A random sample of 243 house loans issued by this bank finds that 42 of them are in default. Do the data indicate that the proportion of loans in default exceeds 14%?

(a) State the null and alternative hypotheses for the test.

(b) State the formula for the test statistic and compute its value. Justify your answer.

(c) Construct the rejection region and make a decision. Use α = 0.05

(d) State a conclusion about the the proportion of house loans in default based on the test you performed.

Answer 1

a)

H0: p = 0.14

Ha: p > 0.14

b)

Sample proportion = 42 / 243 = 0.1728

Test statistics

z = ( - p ) / sqrt [ p ( 1 - p) / n ]

= ( 0.1728 - 0.14) / sqrt [ 0.14 ( 1 - 0.14) / 243 ]

= 1.47

c)

Critical value at 0.05 level = 1.645 ( From Z table)

Rejection region = Reject H0 if z > 1.645

d)

Fail to reject H0.

Since test statistics falls in non-rejection region , we do not have sufficient evidence to

support the claim that the proportion of loans in default exceeds 14%