James was eating a bag of candies that came in eightdifferent colors. He noticed that there appeared to be far fewergreen candies than any of the other colors and wondered if the trueproportion of green candies was lower than the 12.5% that would beexpected if all of the candies came in even amounts. For the sakeof statistics, he decided that he would need to buy more candy totest his hypothesis. James randomly selected several bags andcandies and recorded the color of each piece of candy. He foundthat out of the first 400 candies that he chose, 39 of them weregreen.
James conducts a one-proportion hypothesis test at the 5%significance level, to test whether the true proportion of greencandies was lower than 12.5%.
(a) H0:p=0.125; Ha:p<0.125, which is a left-tailedtest.
(b) Use a TI-83, TI-83 plus, or TI-84 calculator to test whetherthe true proportion of green candies is less than 12.5%. Identifythe test statistic, z, and p-value from the calculator output,rounding to three decimal places.
