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Spring 2011
Math 227
Test #3(Honors)
Name: ___________________
Total: 100 points. 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. (10) Anthropometric survey data are used to publish values that can be used in designing products that are
suitable for use by adults. According to Gordon, Churchill, et al., women have heights with a mean of
64.1 in. and a standard deviation of 2.52 in. The sample of 40 heights of women has a mean of 63.20 in.
and a standard deviation of 2.74 in. Assume the sample is selected from a normally distributed
population. Use a 0.01 significance level to test the claim that this sample is from a population with a
standard deviation equal to 2.52 in.
2. (12) Component of Hypothesis testing.
a. Find the critical values.
Assume that the normal distribution applies. Right-tailed test;   0.05 . Find the critical values.
b. Find the critical values.
Assume that t-distribution applies. Left-tailed test;   0.01 , and n = 15. Find the critical values.
c. Find P-value. The test statistic in a two-tailed test is z = -3.02.
d. Write the clam in symbolic form (include null hypothesis and alternative hypothesis).
The mean annual income of employees who took a statistics course less than $60,000.
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3.
(8) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly
selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct the 95% confidence interval for the standard deviation of the scores of all subjects. Assume
that the population has a normal distribution.
4. (18) The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed
below. Assume that the sample is randomly selected from a population with a normal distribution.
14.6
13.8
14.1
13.7
14.0
14.4
13.6
14.2
a. (8) Construct a 99% confidence interval for the mean amount of cereal in all such packet.
b. (10) A cereal company claims that the mean weight of the cereal in its packets is 14 oz.
Test the claim at the 0.05 significance level.
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5. (10) A supplier of CDs claims that no more than 1% of the CDs are defective. In a randomly sample of
600 CDs, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation.
At the 0.01 level of significance, test the supplier’s claim that no more than 1% are defective.
6. (10) List below are the heights of candidates who won presidential elections and the heights of the
candidates with the next highest number of popular votes. The data are in chronological order so the
corresponding heights from the two lists are matched. A well-known theory is that winning candidates
tend to be taller than the corresponding losing candidates, use a 0.05 significance level to test that theory.
Does height appear to be an important factor in winning the presidency? Assume that pair of values have
difference that are from a normally distributed population.
Won Presidency:
71 74.5
74
73
69.5
71.5
75
72
70.5
69
74
70
71
72
Runner-Up
73 74
68
69.5
72
71
72
71.5
70
68
71
72
70
72
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7. (6) What sample size is needed to estimate the mean white blood cell count for the population of adults in
the United States? Assume that you want 95% confidence that the sample mean is within 0.2 of the
population mean. The population standard deviation is 2.5.
8. (10) 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 95% 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
Female:
14
4
4
7
4
9
15
3
10
1
5
7
12
18
3
1
12
6
4
3
5
5
7
1
9
21
7
6
4
7
2
1
2
14
5
15
9. (6) You have been hired by a consortium of dairy farmers to conduct a survey about the consumption of
milk. If you want to estimate the percentage of adults who drink milk daily, how many adults must you
survey if you want 99% confidence that your percentage is in error by no more than two percentage
points?
10. (10) A survey of 436 workers showed that 192 of them said that it was seriously unethical to monitor
employee e-mail. When 121 senior-level bosses were surveyed, 40 said that it was seriously unethical to
monitor employee email. Use a 0.01 significance level to test the claim that for those saying that
monitoring e-mail is seriously unethical, the proportion of employees is greater than the proportion of
bosses.
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