Question

Chapter Exercise 9-86 A sample of 111 mortgages approved during the current year showed that 46 were issued to a single-earner family or individual. The historical percentage is 38 percent. At the .05 level of significance in a right-tailed test, has the percentage of single-earner or individual mortgages risen? (6-1) H: 3.38 versus H: >.38. Choose the right option. a. Reject He if Zcalc > 1.645 b. Reject He if Zcalc<1.645 (a-2) Calculate the test statistic. (Round Intermedlate calculations to 2 decimal places. Round your answer to 4 declmal places.) Test statistic D (-3) The null hypothesis should be rejected. True False (b) Is this a close decision? Yes NO (c) State any assumptions that are required. a. n b.n C d.n <10 and n(1 - ) > 10 <10 and n(1- ) <10 > 10 and n(1-1) > 10 > 10 and n(1- ) <10 OOOO

Answer 1

Given that, n = 111 and x = 46

=> sample proportion $(\hat p)$ = 46/111 = 0.4144

a-1) The null and alternative hypotheses are,

H0 : π ≤ 0.38 versus H1 : π > 0.38

critical value at significance level of 0.05 is, z* = 1.645

Decision Rule : Reject H0 if Z​​​​​​calc > 1.645

a-2) Test statistic is,

0.414-0.38 =0.75 ¥ 0.38+(1-0.38) 111

=> Test statistic = 0.75

a-3) Since, test statistic = 0.75 < 1.645, we fail to reject the null hypothesis.

Answer : False

b) No, this is not close decision.

c) assumption is,

nπ > 10 and n(1 - π) > 10

Answer : c)