Statistics

17.7 in a survey about satisfaction with local phone service, those
respondents who rated their current service as excellent and those who
rated it Poor- Very Poor were asked to

classify their current local service provider. The results are given in
the table below:

Type of Company

Service Source Long Distance Local Phone Power Cable TV Cellular
Phone

Excellent 264 444 131 215 198

Poor-Very Poor 1394 1318 485 431 572

(a) Set up the hypotheses to test whether the proportion of people who
rated their company as excellent is the same for each type of company.

(b) Calculate the overall proportion of people who rate their current
phone service as excellent

(c) Find the expected frequency for each cell and calculate the
chi-square test statistic.

(d) If you wanted to perform the test at the 0.05 level of significance,
what would the critical value of the test be?

(e) At the 0.05 level of significance, is there a difference in the
proportion of people who rate their local phone service as excellent
among the different types of companies?

17.12 A company that depends heavily on advertising for selling its
products wants to know if its various advertising media have different
effectiveness relative to the age of the customer. The company uses its
warranty return cards to collect the following information:

Age of Customer

Type of

Advertisement 21-30 31-40 41-50 Over 50 Totals

Store display 21 28 8 6 63

Catalog 8 5 1 1 15

Magazine 1 23 8 1 33

Newspaper 18 14 2 4 38

Totals 48 70 19 12 149

(a) Set up the hypotheses to test whether type of advertisement and age
of customer are independent.

(b) What population will the test apply to?

(c) Calculate the expected frequencies for each cell.

(d) How many degrees of freedom will the test have?

(e) Without collapsing any cells, calculate the value of the chi-square
test statistic.

(f) At the 0.05 level of significance, are type of advertisement and age
of customer independent?

(g) Do you think that categories should have been collapsed? Why or why
not?

(h) What categories would you recommend collapsing to fix the problem?

18.2 An Internet service provider is asking customers to rate its
current service. Company of- facials are interested in knowing whether
people who have been customers for more than a year are less satisfied
than new customers (less than six months). They use a 5- point scale
where

1 = Extremely satisfied and 5 = Extremely dissatisfied. The data (al-
ready sorted) are given below:

Old Customers New Customers

I 1

2 1

3 1

3 1

3 1

3 2

3 2

4 3

5 4

4

(b) Set up the hypotheses to see whether the old customers are less
satisfied than the new customers.

(c) Find the ranks for each data value and the rank sum for each sample

(d) At the 0.05 level of significance, what can you conclude?