Hypothesis Testing
1.University of is concerned that out of
state students may be receiving lower grades than students. Two
independent random samples have been selected: 175 observations from population
1 (Out of state students) and 187 from population 2 ( students). The
sample means obtained are X1(bar)=85 and X2(bar)=86. It is known from
previous studies that the population variances are 9.2 and 8.3 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 |
Number |
|
1 |
$77,430.00 |
5,902,000 |
|
2 |
62,620 |
3,800,000 |
|
3 |
69,580 |
3,299,000 |
|
4 |
50,670 |
2,430,000 |
|
5 |
69,180 |
3,367,000 |
|
6 |
73,140 |
5,011,000 |
|
7 |
83,370 |
6,888,000 |
|
8 |
78,880 |
4,935,000 |
|
9 |
64,990 |
5,555,000 |
|
10 |
77,230 |
4,654,000 |
|
11 |
61,380 |
5,598,000 |
|
12 |
62,900 |
2,967,000 |
|
13 |
63,270 |
2,899,000 |
|
14 |
89,190 |
4,245,000 |
|
15 |
60,030 |
4,934,000 |
|
16 |
79,210 |
3,853,000 |
|
17 |
65,770 |
5,625,000 |
|
18 |
84,530 |
6,778,000 |
|
19 |
79,760 |
5,999,000 |
|
20 |
82,640 |
7,834,000 |
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 5,800,000. (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 |
86 |
|
94 |
86 |
78 |
|
91 |
75 |
79 |
|
88 |
83 |
96 |
|
98 |
74 |
97 |
|
84 |
72 |
|
|
90 |
