The U.S. Food and Drug Administration (FDA) bans the use of hormones in poultry

Question

The U.S. Food and Drug Administration (FDA) bans the use of hormones in poultry production. Nevertheless, a recent University of California study found the 10% of the consumers surveyed said that they ate less poultry because of concern over hormones. To check on this claim, 84 consumers are randomly selected and it is found that ten of them eat less poultry because of their concern over hormones. Should we reject the results of the University of California study? (Use a 5% level of significance and be sure to include the critical values and test statistic in your answer)

a. Give the null and alternative hypothesis.
b. Give the test statistic and critical values.
c. Would you reject the null or fail to reject the null hypothesis?

Explanation / Answer

Given n=84, phat=10/84 = 0.119

a. Give the null and alternative hypothesis.

Ho:p=0.1
Ha:p not equal to 0.1

b. Give the test statistic and critical values.

Z=(phat - p)/[p*(1-p)/n]

=(0.119-0.1)/sqrt(0.1*0.9/84)

=0.58

The critical values is Z(0.025)=-1.96 and Z(0.975)=1.96 (check standard normal table)

c. Would you reject the null or fail to reject the null hypothesis?

Since Z=-1.96<0.58<1.96, we do not reject Ho.

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