Question

Past experience is that when individuals are approached with a request to fill out and return a particular questionnaire in a provided stamped and addressed envelope, the response rate is 41%. An investigator believes that if the person distributing the questionnaire is stigmatized in some obvious way, potential respondents would feel sorry for the distributor and thus tend to respond at a rate higher than 41%. To test this theory, a distributor wore an eye patch. Of the 200 questionnaires distributed by this individual, 105 were returned. Does this provide evidence that the response rate in this situation is greater than the previous rate of 41%? State and test the appropriate hypotheses at significance level 0.05.

State the appropriate null and alternative hypotheses.

H₀: p = 0.41 versus H_a: p > 0.41

H₀: p ≠ 0.41 versus H_a: p = 0.41

H₀: p = 0.41 versus  H_a: p ≠ 0.41

H₀: p = 0.41 versus H_a: p < 0.41

H₀: p < 0.41 versus H_a: p > 0.41

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.)

State the conclusion in the problem context.

Reject H₀. We do not have convincing evidence that more than 41% of all people who could be approached with a questionnaire will respond when the distributor wears an eye patch.

Do not reject H₀. We do not have convincing evidence that more than 41% of all people who could be approached with a questionnaire will respond when the distributor wears an eye patch.    

Do not reject H₀. We have convincing evidence that more than 41% of all people who could be approached with a questionnaire will respond when the distributor wears an eye patch.

Reject H₀. We have convincing evidence that more than 41% of all people who could be approached with a questionnaire will respond when the distributor wears an eye patch

Answer 1

Here claim is that the response rate in this situation is greater than the previous rate of 41%

So hypothesis is

H₀: p = 0.41 versus H_a: p > 0.41

So test statistics is

P value is

As P value is less than alpha=0.05, we reject the null hypothesis

So correct answer is  

Reject H₀. We have convincing evidence that more than 41% of all people who could be approached with a questionnaire will respond when the distributor wears an eye patch