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 750 observations from population 1 (female high school teachers) and 710 from population 2 (male high school teachers). The sample means obtained are X1(bar)=$45 k and X2(bar)=$47 k. It is known from previous studies that the population variances are 3.6 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.
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 asthma. He wonders whether there is a strong relationship between the amount of money spent on television advertising for this new drug called XBC 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.
Month Advertising Cost (thousands of dollars), x Number of Orders, y
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.
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.
3. The Course Manager 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 .01 significance level, can she conclude that there is a difference between how well the different tutorials work for the students?
PowerPoint Tutorial AuthorGen Tutorial ABC Tutorial
98 79 65
95 76 73
91 72 78
87 82 96
98 91 97