Question

Your company has a policy of hiring lawyers that can win more than 75% of their cases. Mr. John applied for the job. You take a ramdom sample of 12 of his cases in the past three years. He won 10 of the cases and lost 2 of them. What is the null hypothesis? What is the hypothesis test using an alpha level of 0.05. What's your conclusion? Should Mr. John be hired?

Answer 1

Given that the lawyer will only be hired if winning percentage is more than 75%

so, it is a right tailed hypothesis

Ho: p = 0.75

Ha: p>0.75

sample proportion p(hat) = 10/12 = 0.8333

sample size n = 12

population proportion po = 0.75

test statistic =

using z table to find 0.6 in the left most column and 0.07 in the top most row, we get

p value = 0.2514

p value is greater than 0.05, so we failed to reject the null hypothesis

we can can say that there is insufficient to conclude to that the proportion is greater than 75%

No, Mr. John should not be hired as proportion is not significantly higher than 75%