Problem Set #3

Problem Set #3

Hypothesis Testing

1.University of University College is concerned that out of state students may be receiving lower grades than students. Two independent random samples have been selected: 165 observations from population 1 (Out of state students) and 177 from population 2 ( 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 pharmaceutical company would like to determine if the company 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	$74,430.00	2,856,000
2	62,620	1,800,000
3	67,580	1,299,000
4	53,680	1,510,000
5	69,180	1,367,000
6	73,140	2,611,000
7	85,370	3,788,000
8	76,880	2,935,000
9	66,990	1,955,000
10	77,230	3,634,000
11	61,380	1,598,000
12	62,750	1,867,000
13	63,270	1,899,000
14	86,190	3,245,000
15	60,030	1,934,000
16	79,210	2,761,000
17	67,770	1,625,000
18	84,530	3,778,000
19	79,760	2,979,000
20	84,640	3,814,000

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 2,300,000. (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.Dr. Michaella Evans, a statistics professor at the University of University College, drives from her home to the school every weekday. She has three options to drive there. She can take the Beltway, or she can take a main highway with some traffic lights, or she can take the back road, which has no traffic lights but is a longer distance. Being as data-oriented as she is, she is interested to know if there is a difference in the time it takes to drive each route.

As an experiment she randomly selected the route on 21 different days and wrote down the time it took her for the round trip, getting to work in the morning and back home in the evening. At the .01 significance level, can she conclude that there is a difference between the driving times using the different routes?

Time (in minutes) it took to get to work and back using:

Beltway	Main highway	Back road
88	79	86
94	86	78
91	75	79
88	83	96
98	74	97
84	72	73
90		68
77

You can check your critical value with the following table:http://www.statsoft.com/textbook/distribution-tables

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 increase your error rate and the actual significance level will be different from the desired one.

Please see the Excel formatting tips in the overview.
For questions 2 and 3 you will need the data analysis tools in Excel.
First, make sure that the data analysis tools are added to Excel.
Open Excel and click on tools. One of the menu items should be "Data Analysis". If it is not there, you need to add it.
Click on "add-ins". In the window that opens check the first two items:
"Analysis Toolpak " and "Analysis Toolpak – VBA". Click OK.
Now open the tools menu again, and you will see the data analysis entry
If you have any problems with installing the data analysis tools, go to the Microsoft site:

OVERVIEW

. You will use Excel to solve the statistics problems. It is EXTREMELY important that you prepare a written discussion of each problem to accompany the numerical calculations. You should attach the Excel file in your Assignment folder.

Please make sure that you use only one Workbook for your response. You can create several spreadsheets or tabs under the one Workbook. This will allow me to download one file with all your responses. It would also help if you could make sure your response is contained within the 8.5 by 11 layout. This means that none of your response will cross over several pages. You can also highlight your final answer to assist with the grading. You can use comments and text within the spreadsheet to explain your responses. Please print out your assignment to ensure that it meets the formatting requirements and is
readable.