Questions 39 through 44 are based on the following scenario.
A random sample of 100 college students was interviewed. They were asked what size pizza they usually order and what there favorite topping is. The results are presented below.
Topping
Size
Pepperoni
Cheese
Sausage
Total
Small
18
11
6
35
Medium
14
12
7
33
Large
3
9
20
32
Total
35
32
33
100
Is the pizza topping independent of pizza size? Perform the appropriate test by answering the following questions.
39.State the null hypothesis.
40.Calculate the expected counts and put them in a table similar to the one above.
41.What is the value of the test statistic?
42.What are the degrees of freedom for the distribution of the test statistic of question 41?
43.What is the 95th percentile of the chi-square distribution with the number of degrees of freedom from question 42?
44.Is the observed test statistic greater than the 95th percentile? What does that mean with respect to the test?
Questions 45 through 50 are based on the following scenario.
A consulting firm is determined to find out for one of its clients, a telephone company, if people with different calling plans, think differently about the company. The consulting firm randomly selects 100 customers from each of the three main calling plans and another 50 customers with yet another calling plan, different from the 3 main ones. Each of the selected customers is asked to rate how satisfied they are with the telephone company on a 1 to 5 scale; 1 meaning not at all satisfied and 5 meaning very satisfied.
45.Fill in the blank. The appropriate test to conduct is the chi-square test of .
(a)goodness of fit
(b)homogeneity
(c)independence
46.If 35 people rated to be not at all satisfied with the telephone company, calculate how many of those people you expect to have come from calling plan 1, 2, 3, and the “other” category?
47.What are the degrees of freedom associated with the sampling distribution of the test statistic under the null hypothesis?
48.What are the 90th and 95th percentiles of the chi-square distribution with the degrees of freedom from question 47?
49.Suppose the observed test statistic value is . Are the results statistically significant at the 5% significance level? Are the results statistically significant at the 10% significance level?
50.Explain the difference in your answers to the questions in 49. Include the words “Type I error” and “probability” in your answer.