1. The scores on an aptitude test required for entry into a certain job position have a mean of 500 and a standard deviation of 120. If a random sample of 36 applicants has a mean of 546, is there evidence that their mean score is different from the mean that is expected from all applicants?
(i) Do problem number 1 assuming that the sample size is 16.
2. The training department of a company wishes to determine if there is any difference in the performance between the workers that have completed a training program and those that have not completed the program. A sample of 100 trained workers reveals an average output of 74.3 parts per hour with a sample standard deviation of 16 parts per hour. A sample of 100 who have not been trained has an average output of 69.7 parts per hour with a standard deviation of 18 parts per hour. Is there evidence of a difference in output between the two groups? Write a 95% confidence interval estimate of the difference.
3. The manager of a consulting firm in Lansing, Michigan, is trying to assess the effectiveness of computer skills training given to all new entry-level professionals. In an effort to make such an assessment, he administers a computer skills test immediately before and after the training program to each of 20 randomly chosen employees. The pre-training and post-training scores of these 20 individuals are shown in the table below.
|
Employee
|
Score before
|
Score after
|
|
1
|
62
|
77
|
|
2
|
63
|
77
|
|
3
|
74
|
83
|
|
4
|
64
|
88
|
|
5
|
84
|
80
|
|
6
|
81
|
80
|
|
7
|
54
|
83
|
|
8
|
61
|
88
|
|
9
|
81
|
80
|
|
10
|
86
|
88
|
|
11
|
75
|
93
|
|
12
|
71
|
78
|
|
13
|
86
|
82
|
|
14
|
74
|
84
|
|
15
|
65
|
86
|
|
16
|
90
|
89
|
|
17
|
72
|
81
|
|
18
|
71
|
90
|
|
19
|
85
|
86
|
|
20
|
66
|
92
|
(i) Using a 10% level of significance, do the given sample data support that the firm's training programs is effective in increasing the new employee's working knowledge of computing?
(ii) Re-do using a 1% level of significance.
4. A marketing research consultant hired by Coca-Cola is interested in determining if the proportion of customers who prefer Coke to other brands is over 50%. A random sample of 200 consumers was selected from the market under investigation, 55% favored Coca-Cola over other brands. Additional information is presented below.
Sample proportion 0.55
Standard error of sample proportion 0.03518
Z test statistic 1.4213
p-value 0.07761
|
Sample proportion
|
0.55
|
|
Standard error of sample proportion
|
0.03518
|
|
Z test statistic
|
1.4213
|
|
p-value
|
0.07761
|
|
|
|
(i) If you were to conduct a hypothesis test to determine if greater than 50% of customers prefer Coca-Cola to other brands, would you conduct a one-tail or a two-tail hypothesis test? Explain your answer.
(ii) How many customers out of the 200 sampled must have favored Coke in this case?
(iii) Using a 5% significance level, can the marketing consultant conclude that the proportion of customers who prefer Coca-Cola exceeds 50%? Explain your answer.
(iv) If you were to use a 1% significance level, would the conclusion from part c change? Explain your answer.
5. The following table shows the Height (x) vs. Femur Length (y) measurements (both in inches) for 10 men:
Calculate the coefficient of correlation
|
x
|
70.8
|
66.2
|
71.7
|
68.7
|
67.6
|
69.2
|
66.5
|
67.2
|
68.3
|
65.6
|
|
y
|
42.5
|
40.2
|
44.4
|
42.8
|
40
|
47.3
|
43.4
|
40.1
|
42.1
|
36
|
6. Suppose a crime scene investigator digs up the femur of a man and finds that it is 38.5 inches long. Based on our regression line for the height vs. femur length data, what would we estimate the man's height to have been?
7. A researcher wants to know if there is a relationship between the number of shopping centers in a state and the retail sales (in billions $) of that state. A random sample of 8 states is listed below. After determining, via a scatter-plot, that the data followed a linear pattern, the regression line was found. Using the given data and the given regression output answer the following questions.
State Num Sales
1 630 15.5
2 370 7.5
3 616 13.9
4 700 18.7
5 430 8.2
6 568 13.2
7 1200 23.0
8 2976 87.3
a. What is the equation of the regression line?
b. Interpret the slope in the words of the problem.
c. Find r2 and interpret its meaning in the words of the problem.
d. Find the error for predicting the sales of a state with 1200 stores.
e. Use the regression line to predict the sales for a state with 100 stores
8 A pharmaceutical company is investigating the relationship between advertising expenditures and the sales of some over-the-counter (OTC) drugs. The following data represents a sample of 10 common OTC drugs. Find the equation of the regression line, using Advertising dollars as the independent variable and Sales as the response variable. Interpret the slope of the line in the words of the problem. Find r2 and interpret it in the words of the problem. Use the line to predict the Sales if Advertising dollars = $50 million. Note that AD = Advertising dollars in millions and S = Sales in millions $.
AD S
22 64
25 74
29 82
35 90
38 100
42 120
46 120
52 142
65 180
88 230