A mobile phone service provider randomly samples customers each year to measure current satisfaction with the service provided. The following table summarizes a portion of the survey, with 100 customers sampled each year. Customers are labeled “very satisfied” if they rate their service as 8, 9, or 10 on a 10-point scale. Those who rate the service 5, 6, or 7 are labeled “satisfied. “The rest are labeled “unsatisfied.”

(a) Would the phone provider prefer these counts to be dependent or independent?

(b) The survey includes 100 customers each year, fixing the column totals. Do such fixed margins violate the assumptions of the chi-squared test?

(c) Does it appear that the level of satisfaction and year of the survey are independent or dependent? Don’t calculate ; just skim the table.

(d) Suppose that the values shown in the cells of table were column percentages rather than counts, with 250 surveyed each year. How would the value of  change?

You do it

In each of the next six exercises, answer the question about the small contingency table shown with each exercise.