Problem Set 3 – Fall 2012
Hypothesis Testing
1.
The Connecticut Board of Education is concerned that first year male elementary
school teachers are receiving lower salaries than their female counterparts. Two
independent random samples have been selected: 720 observations from population 1
(male elementary school teachers) and 710 from population 2 (female elementary
school teachers). The sample means obtained are X1(bar)=$35 k and X2(bar)=$36 k. It
is known from previous studies that the population variances are 5.6 and 4.0
respectively. Using a level of significance of .10, is there evidence that the first year
male elementary 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
$99,430.00
2,902,000
2
72,620
3,800,000
3
99,580
3,299,000
4
60,670
2,430,000
5
99,180
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
92,900
2,967,000