Statistical Homework
For questions 2 and 3 you will need the data analysis tools in Excel. please also give lament, simple explanation of how to solve problem.
In question 2 you will use the regression function from the data analysis tools. Carefully read the problem to figure out which is the dependent variable and which is the independent variable. In parts c, e, and f you are asked to interpret the meaning of different measures. This is where you can show your understanding.
In question 3 you will perform hypothesis testing on multiple populations. Be very careful with selecting the test statistic. Tackling question 3 as a series of pair wise comparisons is not the correct way to solve this problem. This will build an error and the actual significance level will be different from the desired one.
1. The Connecticut Board of Education is concerned that first year female High school teachers are receiving lower salaries than their male counterparts. Two independent random samples have been selected 630 observations from population 1 (female high school teachers) and 610 from population 2 (male high school teachers). The sample means obtained are X1(bar)=$46 k and X2(bar)=$47 k. It is known from previous studies that the population variances are 4.1 and 5.0 respectively. Using a level of significance of .05, is there evidence that the first year female high 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 $69,430.00 2,902,000
2 72,620 3,800,000
3 79,58 0 3,299,000
4 60,670 2,430,000
5 69,180 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 52,900 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
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 5,100,000. (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 610 wants to use a new tutorial to teach the students about business ethics. 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 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 a Business Ethics test. At the .01 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 79 66
94 76 78
91 75 79
88 83 96
98
