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Fall 2010
Math 227
Test #3
Name: ___________________
For confidence interval, please write down the critical value(s) and margin of error (if needed), then
write the confidence interval. For Hypothesis testing, use either the traditional method or the P-value
method.
1.
(7)
The department of Mathematics at a four-year university wants to estimate the average
age of students who apply to their graduate program with 98% confidence level. If the
standard deviation of the ages is known to be 10 years of age with a margin of error of 2
years, how large must the sample be?
2.
(12) According
to Crime in the United States, a publication of the FBI, the mean value lost to
purse snatching was $356 in 2008. For last year, 12 randomly selected purse-snatching offenses
yielded the following values lost, to the nearest dollar. At the 5% significance level, test the
claim that the mean value lost to purse snatching has decreased from the 2008 mean. Assume
the population has normal distribution.
231 446
296
386
189 293
261 250
229
372
290 454
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3.
The U.S. National Center for Health Statistics compiles data on the length of stay by patients
in short-term hospitals. Independent random samples of 39 male patients and 35 female patients
gave the following data on the length of stay, in days. Construct a 90% confidence interval for
the difference between the two means. Can you conclude that, on average, the lengths of stay in
short-term hospitals by males and females differ?
Male:
4
4
12
18
9
6
12
10
3
6
15
7
3
13
1
2
10
13
5
7
1
23
9
2
1
17
2
24
11
14
6
2
1
8
1
3
19
3
1
(15)
Female:
14
4
4
4.
7
4
9
15
3
10
1
5
7
12
18
3
1
12
6
3
5
5
7
1
9
21
7
6
4
7
2
1
2
14
5
15
A Statistics major attending UCLA wants to take a survey of families who like Math. He
wants to be 96% sure that the true proportion of families who like Math is no more than 1.5% of
the true proportion. Compute the sample size if she has some idea of past research about the
estimate of this proportion and that is 25%.
(7)
2
5.
(15) In
one trip of the Royal Caribbean cruise ship Freedom of the Seas, 338 of the 3823
passengers become ill with a Norovirus. AT about the same time, 276 of the 1652 passengers on
the Queen Elizabeth II cruise ship became ill with a Norovirus. Treat the sample results as a
simple random sample from large populations, and use a 0.01 significance level to test the claim
that the rate of Norovirus illness on the Freedom of the Seas is less than the rate on the Queen
Elizabeth II.
6.
(10)
In a poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all
incomes on tax returns. Construct a 95% confidence interval estimate of the percentage of all
adults who have that belief.
3
7.
(12)A
simple random sample of 32 cars yields a mean weight of 3605.3 lbs, a standard deviation
of 501.7 lbs., and the sample weight appear to be from a normal distributed population. Use a
0.01 significance level to test the claim that the standard deviation of the weights of cars is less
than 520 lbs.
8.
(10)
Listed below are weights (in pounds) of glass discarded in one week by randomly selected
households. The sample weights come from a normal distributed population.
3.52 8.87 3.99 3.64 2.33 3.21 0.25 4.94
a. What is the best point estimate of the weight of glass discarded by all households in one
week?
b. Construct a 95% confidence interval estimate of the mean weight of glass discarded by
all households.
4
9.
Listed below are ten voltage levels recorded in Melanie’s home on ten different days. These
values come from a normally distributed population. Use the sample data to construct a 95%
confidence interval estimate of the standard deviation of all voltage level.
123.3 123.5 123.7 123.4 123.6 123.5 123.5 123.4 123.6 123.8
(10)
10. (6) Find the critical values.
a. Assume that the normal distribution applies. Find the critical values.
Right-tailed test;   0.01 .
b. Assume that t-distribution applies. Find the critical values.
Right-tailed test;   0.01 , and n = 23.
c. Assume that the chi-square distribution applies. Find the critical values.
Right-tailed test;   0.01 , n = 23.
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