BSTAT 202

Recitation: c2 Test Problems

1. An operations professor is interested in studying the attitudes of employees of large auto firms regarding self-managed work teams, where a team is empowered to make decisions such as which team members will perform which tasks needed to get the team’s job done. As part of her research, she asks 80 hourly workers and 40 middle managers about their attitude regarding the self-managed work team concept. Her results are summarized in the following two-way table:

Attitude Towards Self-Managed Work-Teams

Type of Employee / Favor / Neutral / Oppose / Total
Hourly Worker / 45 / 10 / 10 / 80
Middle Management / 15 / 10 / 30 / 40
Total / 60 / 20 / 40 / 120

At the a = 0.01 level of significance, test to see if the employees’ attitudes towards self-managed work teams is independent of employee type.

2. It is becoming common to solicit the opinions of potential users when designing or revising Web sites used by firms that engage in e-commerce. Suppose that a large clothing retailer (L.L. Bauer) is considering four different layouts for its revised Web site. A random sample of n = 80 customers who regularly use the Web to order from L.L. Bauer are asked to try all four layouts and pick their favorite. The results are summarized in the following table:

Preferred
Layout #1 / Preferred
Layout #2 / Preferred
Layout #3 / Preferred
Layout #4
33 / 18 / 10 / 19

(a) At the a = 0.05 level of significance, test to see if customers are indifferent to the type of layout used.

(b) What can you say about the p-value for this test?


Problem 1 Solution: We’re testing H0: Attitude is independent of employee type vs. H1: They’re dependent. Begin by finding expected frequencies for each cell (they’re listed in ()):

Attitude Towards Self-Managed Work-Teams

Type of Employee / Favor / Neutral / Oppose / Total
Hourly Worker / 45 (40) / 10 (13.33) / 10 (26.67) / 80
Middle Management / 15 (20) / 10 (6.67) / 30 (13.33) / 40
Total / 60 / 20 / 40 / 120

Calculate =(45-40)2/40 + (10-13.33)2/13.33 + …. + (30 – 13.33)2/13.33 = 35.64

This statistic has (2 – 1)(3 – 2) = 2 degrees of freedom, so at the 0.01 level the decision rule is to reject H0 if c2calc > 9.210. Since 35.64 > 9.210, we’d reject H0 and conclude that the attitude towards self-managed work teams is related to the type of employee.

Problem 2 Solution: Test H0: Customers are indifferent vs. H1: Customers aren’t indifferent: some layouts are preferred to others.

Under H0, the probability that the customer will choose any particular layout as being preferred is 0.25 (they really don’t care so it’s just a random pick with each layout being equally likely), so the expected frequencies are 20, 20, 20, and 20:

Preferred
Layout #1 / Preferred
Layout #2 / Preferred
Layout #3 / Preferred
Layout #4
33 (20) / 18 (20) / 10 (20) / 19 (20)

Calculate =(33 - 20)2/20 + (18 - 20)2/20 + (10 – 20)2/20 + (19 - 20)2/20 = 13.70.

(a) This statistic has 4 – 1 = 3 degrees of freedom. At the 0.05 level of significance the decision rule is to reject H0 if c2calc > 7.815. Since 13.70 > 7.815, we’d reject H0 and conclude that customers do prefer some layouts over others.

(b) The calculated statistic (13.70) is larger than all values shown on the table for 3 degrees of freedom, so the p-value must be less than 0.01 (that’s the smallest tail probability considered by the table).

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