Problems -
For each of the 7 problems you must do the following steps:
A) State which test you are using and why you should use that test.
B) State the hypotheses (Remember to use the Greek letters, when appropriate).
C) State the rejection rule for your hypothesis test based on the critical value.
D) Calculate the test statistic based on the sample information.
E) Calculate the p-value.
F) State your decision made AND your conclusion in the context of the problem.
G) State the type of error you may have made.
Problem 1 - Anita's nursery specializes in residential custom designed landscapes. The labor cost associated with a project is based on the number of plantings for the trees, shrubs, etc. Managers use 2 hours of labor for planting a medium sized tree. A sample of 19 plantings from the last month were as follows (in hours).
1.9 1.7 2.8 2.4 2.6 2.5 2.8 3.2 1.6 2.5 1.7 1.9 2.3 2.6 2.4 1.7 2.1 2.3 2.5
Use a .05 level of significance to test whether the mean tree planting time exceeds 2 hours. What recommendations would you make to the managers in terms of the planting time for medium trees?
Problem 2 - To investigate savings from buying store brand products versus name brand products, Dr. K and his graduate assistant shopped for a list of items at the local Moorer's Market. One cart was filled with the national brand products and the other cart was filled with the store brand of the same sized items. The cart contents are shown below.
|
Product purchased
|
National brand item price ($)
|
Store brand item price ($)
|
|
Ketchup
|
1.69
|
.79
|
|
Coffee
|
2.79
|
1.59
|
|
Soda
|
2.79
|
1.64
|
|
Paper towels
|
1.39
|
.50
|
|
Ice cream
|
3.99
|
2.59
|
|
Cheese
|
3.99
|
2.99
|
|
Spaghetti
|
.89
|
.53
|
|
Butter
|
2.39
|
1.69
|
|
White rice
|
3.99
|
1.99
|
|
Vegetable oil
|
2.19
|
1.69
|
Use alpha = .05 to determine if the store brand prices is significantly less than the national brand prices.
Problem 3 - Starting annual salaries for new graduates entering the work force were collected for 12 public accountants and 14 financial planners. The data (in thousands of dollars) is shown below.
|
Public Accountant
|
Financial Planner
|
|
30.6
|
31.6
|
|
31.2
|
26.6
|
|
28.9
|
25.5
|
|
35.2
|
25.0
|
|
25.1
|
25.9
|
|
33.2
|
32.9
|
|
31.3
|
26.9
|
|
35.3
|
25.8
|
|
31.0
|
27.5
|
|
30.1
|
29.6
|
|
29.9
|
23.9
|
|
24.4
|
26.9
|
|
|
24.4
|
| |
25.5 |
With an alpha = .05, test to determine if there is a significant difference between the mean starting salaries for the 2 different professions.
Problem 4 - In a test of the quality of 2 different tv commercials, each one was shown in a separate test area 10 times in a week long study. The following week, a phone survey was conducted to see which people had seen the commercials. People who had seen the commercials were asked to recall the primary message for that commercial. The data is shown below.
|
Commercial
|
# who saw the commercial
|
# who recalled the primary message of the commercial
|
|
A
|
150
|
63
|
|
B
|
200
|
50
|
With a significance level of .05, test to see if the proportion of people who were able to recall the primary message from commercial A was greater than the proportion of people who were able to recall the primary message from commercial B.
Problem 5 - A cat food company wants to expand its product line beyond its current kidney and shrimp based cat foods. The company is considering 3 new flavors, including Chicken liver, Salmon and Beef. A sample of 50 cats from a local animal shelter was selected for the experiment. Ten cats were randomly assigned to each of 5 flavors. Each cat was presented with 3 ounces of cat food and the numbers recorded below are the number of ounces of food consumed by the cat within 10 minutes. With alpha = .05, is there evidence of a difference in the mean amount of food eaten among the 5 flavors considered? Do a complete and thorough analysis of the data using SPSS. What are your conclusions about the 5 flavors? Based on your analysis, what should the company do?
|
Kidney
|
Shrimp
|
Chicken Liver
|
Salmon
|
Beef
|
|
2.37
|
2.26
|
2.29
|
1.79
|
2.09
|
|
2.62
|
2.69
|
2.23
|
2.33
|
1.87
|
|
2.31
|
2.25
|
2.41
|
1.96
|
1.67
|
|
2.47
|
2.45
|
2.68
|
2.05
|
1.64
|
|
2.59
|
2.34
|
2.25
|
2.26
|
2.16
|
|
2.62
|
2.37
|
2.17
|
2.24
|
1.75
|
|
2.34
|
2.22
|
2.37
|
1.96
|
1.18
|
|
2.47
|
2.56
|
2.26
|
1.58
|
1.92
|
|
2.45
|
2.36
|
2.45
|
2.18
|
1.32
|
|
2.32
|
2.59
|
2.57
|
1.93
|
1.94
|
Problem 6 - Where people turn to for their news could possibly vary by many different factors including age, gender, race, education level, etc. Information from a study is shown below for where different age groups primarily get their news.
|
Age groups
|
|
|
|
Media source for news
|
Under 36 years
|
36-50 years
|
50 + years
|
|
Local TV
|
107
|
119
|
133
|
|
National TV
|
73
|
102
|
127
|
|
Radio
|
85
|
97
|
109
|
|
Local Paper
|
22
|
59
|
107
|
|
Internet
|
135
|
73
|
56
|
|
|
|
|
At the .05 level of significance, is there evidence of a significant relationship between the age group and where people primarily get their news? If so, explain in detail. What are the managerial implications of this information? Explain.
Problem 7 - The business problem facing a consumer products company is to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, the company is interested in the effectiveness of radio and newspaper advertising (including the cost of discount coupons). During a one month test period, data were collected from a sample of 22 cities with approximately equal populations. Each city is allocated a specific expenditure level for radio advertising and for newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorder and shown in the table below.
You are to do a complete and thorough analysis of this problem, as shown in class. Use SPSS or Excel and alpha = .05 for all tests.
Make sure that you state the regression model, explain how good the model is, state the relationships between the variables, interpret the coefficients, use the model to make a prediction, and assess whether or not any of the underlying model assumptions were met or violated.
|
Sales
|
Radio
|
Newspaper
|
|
973
|
0
|
40
|
|
1119
|
0
|
40
|
|
875
|
25
|
25
|
|
625
|
25
|
25
|
|
910
|
30
|
30
|
|
971
|
30
|
30
|
|
931
|
35
|
35
|
|
1177
|
35
|
35
|
|
882
|
40
|
25
|
|
982
|
40
|
25
|
|
1628
|
45
|
45
|
|
1577
|
45
|
45
|
|
1044
|
50
|
0
|
|
914
|
50
|
0
|
|
1329
|
55
|
25
|
|
1330
|
55
|
25
|
|
1405
|
60
|
30
|
|
1436
|
60
|
30
|
|
1521
|
65
|
35
|
|
1741
|
65
|
35
|
|
1866
|
70
|
40
|
|
1717
|
70
|
40
|
Attachment:- Assignment File.rar