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Graded Homework 7
You have submitted this Homework 6 times (including this time).
You may submit this Homework a total of 40 times and receive full credit.
The first three questions cover tests for the difference between means in dependent
samples, material that can be found in your course packet on pages 5758. The last
five questions are about tests for the difference between two population proportions,
whether the null hypothesis is that the proportions are equal or not. This material can
be found on pages 5861 in your course packet.
Question #1
This question is identical to example #1 on slide 26 (page 57) of your course packet.
To determine whether a new steelbelted radial tires lasts longer than an existing
model, Firestone designs the following experiment.
One tire of each type (an existing model and an old model) were installed on the rear
wheels of 20 randomly selected cars. The number of miles driven by each driver,
until tires wore out, were recorded and are stored
here
.
Hint: first think about whether the two samples are independent or dependent.
What is the relevant point estimate?
4.55
What is the value of the test statistic?
2.817586964
What is the pvalue for this test?
0.00549698
Allowing for a 5% chance of a Type I error, what is your conclusion for this test?
•
Reject the null hypothesis and conclude that new tires last longer.
•
Reject the null hypothesis and conclude there is not enough evidence to
claim that new tires last longer.
•
Do not reject the null hypothesis and conclude there is not enough
evidence to claim that new tires last longer.
•
Do not reject the null hypothesis and conclude that new tires last longer.
Now create a 95% confidence interval for the difference in means of the two
populations.
The lower and upper bounds are
1.17
and
7.93
respectively.
Item 5: Your answer is within ±.0001 of the solution  correct.
Item 6: Your answer is within ±.0001 of the solution  correct.
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Question #2
This question is the same as example #2 on slide 30 (page 58) of the course packet.
In an agricultural experiment, two expensive highyield varieties of corn are to be
tested and yield improvements are to be measured. The experiment is arranged so that
each variety is planted in ten pairs of similar plots. Data is collected on yield
increases obtained for these two varieties.
Plot
Variety
A
Variety
B
1
12.6
10.5
2
9.2
8.1
3
6.4
6.2
4
9.8
10.1
5
15.3
12.2
6
16.1
14
7
12.3
10.1
8
11.3
13.6
9
12.2
9.8
10
14.1
13.4
Which of the following tests should be used?
•
A pooled variance ttest should be used since we have dependent samples.
•
A paired sample ttest should be used since we have dependent
samples.
•
An unequal variance ttest should be used because even though we have
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This note was uploaded on 07/23/2010 for the course ECON 203 taught by Professor Petry during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 Petry

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