Large-Sample Hypothesis Tests for a Population Proportion A) We want to test if

Question

Large-Sample Hypothesis Tests for a Population Proportion

A) We want to test if ABC bank’s default rate is significantly less than 8%. Out of a random sample of 300 customers, 22 customers defaulted. Construct H0 and Ha, and test it with a significant level 5%.

B) We want to test if the approval rate of school tax bill is significantly more than 60%. 1290 out of 2000 randomly selected voters support the bill. Construct H0 and Ha, and test it with a significant level 5%.

C) Calculate the p-value of the test statistic in Exercise A. Is the p-value consistent with the test result? Also test H0 again with = 0.01 and = 0.001.

D) Calculate the p-value of the test statistic in Exercise B. Is the p-value consistent with the test result? Also test H0 again with = 0.01 and = 0.001.

Explanation / Answer

here Ho: p>=0.08

Ha: p<0.08

critical value of test stat at 0.05 level ; z=-1.6449

std error =(p(1-p)/n)1/2 =0.0157

phat=22/300 =0.0733

hence test stat z=(phat-p)/std error =(0.0733-0.08)/0.0157 =-0.4256

as test stat is not in critical region we can not reject null hypothesis

b)Ho:p<=0.6

Ha:p>0.6

critical value =1.6449

std error =0.011

phat=1290/2000 =0.645

hence test stat z=(0.645-0.6)/0.011 =4.107

as test stat is higher then critical value ; we reject null, hypothesis and accept that it is greater then 60%

c) p value=0.3352

yes it is consistent, result is same with = 0.01 and = 0.001. cause p value is higher

d) p value =0.00002

yes , it is consistent result is same with = 0.01 and = 0.001. cause p value is lower then them

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