Stats. Assignment 1

| October 22, 2018

Assignment #4
DUE: April 4, 2012 (Section A), April 5 (Section B)

All
questions are worth 10 marks. Answers
must be submitted using the Answer Template available on the WebCT page for
this course.

Hypothesis
Testing: Differences in Population Means

1. Acme Signal Light company has decided to
install new microprocessors in its traffic light assemblies and has two
potential suppliers from which to choose.
It would like to purchase from both in order to have more than one supply
source, provided there is no difference in durability. A random sample of 35 microprocessors from
Supplier A found a Mean Time to Failure of 2,800 hours. A random sample of 32 microprocessors from
Supplier B found a MTF of 2,750 hours.
Information from industry sources indicates that the population standard
deviation is 200 hours for Supplier A and 180 hours for Supplier B. At the 5% level of significance, test the
null hypothesis that the MTF is equal for these suppliers against the
alternative hypothesis that there is a difference.

2. Discount stores own outlet A and outlet
B. For the past year, outlet A has spent
more dollars advertising widgets than outlet B.
The corporation wants to know if this advertising has resulted in more
sales in outlet A than in outlet B. A
random sample of 36 days at outlet A had a mean of 170 widgets sold per
day. A random sample of 36 days at
outlet B had a mean of 165 widgets per day.
Assuming population standard deviations of sales of 6 widgets at outlet
A and 5 widgets at outlet B, test the null hypothesis that sales are no higher
at outlet A than at outlet B against the alternative hypothesis that sales are
higher at outlet A.

Hypothesis
Testing: Differences in Population Proportions

3. Acme Advertising
was awarded a contract by a city government to communicate the need for
recycling. Before their advertising
campaign, survey results indicated that 36% of the cities residents believed in
recycling. This survey used a sample of
50 individuals. After the campaign, a
follow-up survey of 50 residents found that 24 of them believed in
recycling. At the 1 percent level of
significance, test the hypothesis that the campaign has not had an effect on
attitudes towards recycling (i.e., that belief in recycling has not increased).

4. An automobile manufacturer wants to test
whether the quality of work done in two of its assembly plants is the
same. Random samples of n1 =
300 and n2 = 200 cars were taken from each plant and check for
quality. The samples show 39 problems in
plant 1 and 20 in plant 2. At the 1
percent significance level, test the null hypothesis that the quality of work
done is the same in both plants.

Regression

5. The file Baseball
Stats.xls contains data on the proportion of games won during the 2010
Major League Baseball season for each team and the total salaries paid by each
team that year. Using regression
analysis, answer the following questions:
a.
Is there a statistically significant relationship between salary and
winning?
b.
For each additional thousand dollars spend on salaries, what is the
predicted impact on the winning proportion? (ignore statistical significance)
c.
How much of the variation across teams is explained by salary
differences?

(NOTE:
you can use Excel for the regression or another statistical package such
as Stata or Minitab if you prefer).

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