Question

A restaurant's marketing department claims that 45% of customers prefer hamburgers, 41% of the customers prefer chicken sandwiches, and 14% of the customers prefer fish sandwiches.   To test this claim, a random group of customers at a fast food chain were asked whether they preferred hamburgers, chicken sandwiches, or fish sandwiches, with the results shown below.     

                 Sandwich :          Hamburgers   Chicken Fish
         ------------------------------------------------------------------------
       No. of customers:                  40                 16           8

Based on this sample data, is there evidence to reject the restaurant's claim at a significance level of ? = .05?

Answer 1

Solution: The null and the alternative hypotheses is given below:

Customers preferences are distributed as claimed by the restaurant's marketing department.

Customers preferences are not distributed as claimed by the restaurant's marketing department.

Under null hypothesis, the test statistic is:

Where

is the observed frequency

is the expected frequency

rounded to three decimals

Now value at 0.05 significance level for is

Since , we therefore reject the null hypothesis and conclude that there is evidence to reject the restaurant's claim