# The Man and the Sea

Problem Set #3
Hypothesis Testing

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.

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...