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ANSWERS MUST BE POSTED IN MICROSOFT EXCEL, with a Brief explanation in word with how the problem was solved.
Fall 2013
Problem Set #3
Hypothesis Testing
1. University of Maryland University College is concerned that out of state students may be
receiving lower grades than Maryland students. Two independent random samples have been
selected: 165 observations from population 1 (Out of state students) and 177 from population 2
(Maryland students). The sample means obtained are X1(bar)=86 and X2(bar)=87. It is known
from previous studies that the population variances are 8.1 and 7.3 respectively. Using a level of
significance of .01, is there evidence that the out of state students may be receiving lower
grades? Fully explain your answer.
Simple Regression
2. A CEO of a large plastics manufacturing company would like to determine if she should be
placing more money allotted in the budget next year for television advertising of a new baby
bottle marketed for controlling reflux and reducing gas. She wonders whether there is a strong
relationship between the amount of money spent on television advertising for this new baby
bottle called Gentle Bottle and the number of orders received. The manufacturing process of this
baby bottle is very difficult and requires advanced quality control so the CEO would prefer to
generate a stable number of orders. The cost of advertising is always an important consideration
in the phase I roll-out of a new baby bottle. Data that have been collected over the past 20
months indicate the amount of money spent of television advertising and the number of orders
received.
The use of linear regression is a critical tool for a manager’s decision-making ability. Please
carefully read the example below and try to answer the questions in terms of the problem
context. The results are as follows:
Month Advertising Cost Number of Orders
1 $77,430.00 2,902,000
2 62,620 1,800,000
3 69,580 1,299,000
4 50,670 1,430,000
5 69,180 1,367,000
6 73,140 2,011,000
7 83,370 3,888,000
8 78,880 2,935,000
9 64,990 1,555,000
10 77,230 3,654,000
11 61,380 1,598,000
12 62,900 1,967,000
13 63,270 1,899,000
14 89,190 3,245,000
15 60,030 1,934,000
16 79,210 2,853,000
17 65,770 1,625,000
18 84,530 3,778,000
19 79,760 2,999,000
20 82,640 3,834,000
a. Set up a scatter diagram and calculate the associated correlation
coefficient. Discuss how strong you think the relationship is between the
amount of money spent on television advertising and the number of orders
received. Please use the Correlation procedures within Excel under Tools
> Data Analysis. The Scatterplot can more easily be generated using the
Chart procedure.
NOTE: If you do not have the Data Analysis option under Tools you must install it. You need to
go to Tools select Add-ins and then choose the 2 data toolpak options. It should take about a
minute.
b. Assuming there is a statistically significant relationship, use the least squares method to find
the regression equation to predict the advertising costs based on the number of orders received.
Please use the regression procedure within Excel under Tools > Data Analysis to construct this
equation.
c. Interpret the meaning of the slope, b1, in the regression equation.
d. Predict the monthly advertising cost when the number of orders is 1,800,000. (Hint: Be very
careful with assigning the dependent variable for this problem)
e. Compute the coefficient of determination, r2, and interpret its meaning.
f. Compute the standard error of estimate, and interpret its meaning.
g. Do you think that the company should use these results from the regression to base any
corporate decisions on?….explain fully.
Hypothesis Testing on Multiple Populations
3. The ABC Tutoring Director wants to use a new tutorial to teach middle school students about
basic algebraic techniques. As an experiment she randomly selected 18 students and randomly
assigned them to one of three groups which include either a PowerPoint presentation created by
the classroom teachers, WebEx Presentation created by an outside contractor, or a well known
tutorial by the EducTrain company. After completing their assigned tutorial, the students are
given a basic algebraic methods quiz. At the .01 significance level, can she conclude that there is
a difference between how well the different tutorials work for the middle school students?
Students Grades on the Algebraic Methods Quiz following the Tutorial
PowerPoint Tutorial WebEx Tutorial EducTrain Tutorial
88 79 96
94 86 78
91 75 89
88 83 96
98 74 97
84 72
90
You can check your critical value with the following table:
http://www.statsoft.com/textbook/distribution-tables
