A sample of 102 mortgages approved during the current year showed that 41 were i

Question

A sample of 102 mortgages approved during the current year showed that 41 were issued to a single-earner family or individual. The historical percentage is 33 percent. At the .05 level of significance in a right-tailed test, has the percentage of single-earner or individual mortgages risen? (a-1) H0: 1formula123.mml ? .33 versus H1: 1formula123.mml > .33. Choose the right option. a. Reject H0 if zcalc > 1.645 b. Reject H0 if zcalc < 1.645 a b (a-2) Calculate the test statistic. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal places.) Test statistic=

Explanation / Answer

H0: P < 0.33

H1: P > 0.33

p = 41/102 = 0.40

At alpha = 0.05, the critical value is z0.95 = 1.645

So reject H0, if zcalc > 1.645

The test statistic z = (p - P)/sqrt(P * (1 - P)/n)

                             = (0.40 - 0.33)/sqrt(0.33 * 0.67/102)

                             = 1.5035

As the test statistic value is not greater than the critical value( 1.5035 < 1.645), so the null hypothesis is not rejected.

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