Recent incidents of food contamination have caused great concernamong consumers. An article reported that 39 of 80 randomlyselected Brand A brand chickens tested positively for eithercampylobacter or salmonella (or both), the leading bacterial causesof food-borne disease, whereas 62 of 80 Brand B brand chickenstested positive.
a)Does it appear that the true proportion of non-contaminatedBrand A chickens differs from that for Brand B? Carry out a test ofhypotheses using a significance level 0.01. (Usep1 for Brand A and p2 forBrand B.)
Calculate the test statistic and P-value. (Round yourtest statistic to two decimal places and your P-value tofour decimal places.)
z= P-value =
b)if the true proportions of non-contaminated chickens for theBrand A and Brand B are 0.50 and 0.25, respectively, how likely isit that the null hypothesis of equal proportions will be rejectedwhen a 0.01 significance level is used and the sample sizes areboth 60? (Round your answer to four decimal places.)
