# Statistics

Hypothesis Testing

1. The MBA department is concerned that dual degree students may be receiving lower grades than the regular MBA students. Two independent random samples have been selected 450 observations from population 1 (dual degree students) and 410 from population 2 (MBA students). The sample means obtained are X1(bar) =84 and X2(bar) =86. It is known from previous studies that the population variances are 4.6 and 5.0 respectively. Using a level of significance of .05, is there evidence that the dual degree students are receiving lower grades? 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 (thousands of dollars) Number of Orders

1 $68.93 2,902,000

2 72.62 3,893,000

3 79.58 3,299,000

4 58.67 2,130,000

5 69.18 3,367,000

6 70.14 4,111,000

7 93.37 4,923,000

8 78.88 4,935,000

9 82.99 5,276,000

10 75.23 3,654,000

11 91.38 4,598,000

12 52.90 2,967,000

13 61.27 2,999,000

14 89.19 4,345,000

15 90.03 4,934,000

16 78.21 3,653,000

17 83.77 5,625,000

18 82.53 5,978,000

19 98.76 5,999,000

20 72.64 5,834,000

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. The original Excel CD will be required for this installation. 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 5,000,000. (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 15 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 .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 79 65

85 86 73

91 72 78

87 82 96

98 91 97

https://brainmass.com/statistics/regression-analysis/statistics-404623

#### Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problems. Calculations have been shown both in text and EXCEL for better understanding. The solution provides students with a clear perspective of the underlying concepts.

Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]

having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).

Demonstrate that the mle theta;hat is a sufficient statistic for theta;.

Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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