33. University Dining. The university dining service believes there is no difference in student preference among the following four entrees: pizza, cheeseburgers, quiche, and sushi. A sample of 500 students showed that 250 preferred pizza, 215 preferred cheeseburgers, 30 preferred quiche, and 5 preferred sushi. Test, at level of significance , whether or not there is a difference in student preference among the four entrees. (Hint: For the test of no difference among the proportions, the null hypothesis states that all proportions are equal.)
11.1.33
, , , . : The random variable does not follow the distribution specified in . , , , . Since none of the expected frequencies is less than 1 and none of the expected frequencies is less than 5, the conditions for performing the goodness of ft test are met. . Reject if . . Since , we reject . There is evidence that there is a difference in student preference among the four entries.