In: Statistics and Probability
An article wanted to examine people’s opinion about whether student athletes should be paid to play their sport while in college. From a random sample of 412 people, 218 thought that athletes should be paid to play their sport while in college.
(a) Assuming the sample is representative of population, construct a 94% confidence interval for the proportion of people who believe athletes should be paid to play their sport while in college.
(b) Give an interpretation of the interval that you produced in part (a).
(c) Would you conclude that a majority of people favor paying athletes to play their sport in college? That is set up a test of hypothesis to determine whether more than 50% of people believe student athletes should be paid to play their sport while in college. Clearly indicate you null and alternative hypothesis, test statistic, p-value and conclusion at a 0.05 significance level in the context of the problem.