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Graded Homework 8
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These questions cover hypothesis tests for variances in two populations, material you
can find in your course packet on pages 6164.
Question #1
Please refer to example #1 on slide 46 (page 62) of the course packet.
A regional fast food chain wants to insure that their customers do not eat meat
carrying E.coli bacteria. The preventive measure is to cook the meat at the required
temperature. Because of varying patty size and burner temperatures, meats cooked for
the same length of time can have different final internal temperatures. The health
department is recommending that the newer, digitally controlled burners reduce the
variation in the final internal temperatures. There are two models of digitally
controlled burners to choose from. The restaurant chain will choose the model with
the most consistent final internal temperature of meets cooked. They sample 11
batches of meat cooked by burner model 1, and 13 batches of meat cooked by burner
model 2. They found S
1
2
=6.7, and S
2
2
=2.5.
Is there a difference in temperature consistency at the 10% level of significance?
1.
The appropriate test that the restaurant chain owner would have to perform by
is the:
ftest for the ratio of variances
.
2.
What's the value of the appropriate test statistic for this test?
2.68
3.
What's the p value for this test?
0.109043655
4.
Can the restaurant chain owner conclude at the 5% significance level that
variances are unequal?
no
5.
For a 95% confidence interval, the lower and upper confidence limits are
.794417733 = 0.794417733
and
9.704146
respectively.
Item 5: Your answer is within ±0.1% of the solution  correct.
Item 6: Your answer is within ±0.1% of the solution  correct.
You received a raw score of 100% on this question.
Question #2
Please refer to example #2 on slide 49 (page 63) of the course packet.
The returns of two portfolios were recorded for ten years. Portfolio 1 had a variance
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View Full Documentof returns of 295, while portfolio 2 had a variance of 105. Can we conclude at a 5%
level of significance that portfolio 1 is riskier (has a higher variance) than portfolio 2?
1.
The test statistic for testing this claim will have the following distribution:
o
F distribution with 9 and 9 degrees of freedom
o
Chisquared distribution with 9 degrees of freedom
o
F distribution with 10 and 10 degrees of freedom
o
Chisquared distribution with 10 degrees of freedom
2.
The value of the test statistic for testing the hypothesis is
2.80952381
.
3.
The pvalue associated with this test statistic is
0.069881665
.
4.
Based on your results, what is your conclusion?
o
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 Spring '08
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