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Hypothesis Testing Custom Essay

Hypothesis Testing
1. The Connecticut Board of Education is concerned that first year male elementary school teachers are receiving lower salaries than their female counterparts. Two independent random samples have been selected: 720 observations from population 1 (male elementary school teachers) and 710 from population 2 (female elementary school teachers). The sample means obtained are X1(bar)=$35 k and X2(bar)=$36 k. It is known from previous studies that the population variances are 5.6 and 4.0 respectively. Using a level of significance of .10, is there evidence that the first year male elementary school teachers are receiving lower salaries? Fully explain your answer.
Simple Regression

2.  A CEO of a large pharmaceutical company would like to determine if he should be placing more money allotted in the budget next year for television advertising of a new drug marketed for controlling diabetes. He wonders whether there is a strong relationship between the amount of money spent on television advertising for this new drug called DIB and the number of orders received. The manufacturing process of this drug is very difficult and requires stability 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 drug. 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

$99,430.00

2,902,000

2

72,620

3,800,000

3

99,580

3,299,000

4

60,670

2,430,000

5

99,180

3,367,000

6

73,140

4,011,000

7

93,370

4,888,000

8

78,880

4,935,000

9

94,990

5,555,000

10

77,230

3,654,000

11

91,380

5,598,000

12

92,900

2,967,000

13

63,270

2,899,000

14

89,190

4,245,000

15

90,030

4,934,000

16

79,210

3,853,000

17

85,770

5,625,000

18

84,530

5,778,000

19

99,760

5,999,000

20

102,640

6,834,000

  1. 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 two data tool pack 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 4,800,000. (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.
Hypothesis Testing on Multiple Populations

3. The Course Manager for AMBA 660 wants to use a new tutorial to teach the students about environmental sustainability. As an experiment she randomly selected 38 students and randomly assigned them to one of three groups which include either a PowerPoint presentation created by the faculty, AuthorGen Presentation created by the faculty, or a well known tutorial by the ABC company. After completing their assigned tutorial, the students are given an Environmental Sustainability quiz. At the .10 significance level, can she conclude that there is a difference between how well the different tutorials work for the students?

Students Grades on the Business Ethics Test following the Tutorial

PowerPoint Tutorial

AuthorGen Tutorial

ABC Tutorial

98

89

96

94

86

78

91

75

79

88

83

96

98

74

97

91

92

90

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