Sample Final Exam Questions for Stat 104
INSTRUCTIONS: Read the questions carefully and completely. Answer each question and show
work in the space provided. Partial credit will not be given if work is not shown. When asked to
explain, describe, or comment, do so within the context of the problem.
1. [18 pts] In the Gallup Poll for April 16-18, 2004, 520 out of the 1000 adults 18 and older
surveyed approved of the job President Bush is doing as president.
(a) [2] What is the population the Gallup Poll is surveying?
(b) [3] Calculate a 95% confidence interval for the population proportion of adults 18 and
older that approve of the President’s job performance.
(c) [4] Give an interpretation of the confidence interval you calculated in part b).
(d) [9] Test the hypothesis that the population proportion of adults who approve of the job
President Bush is doing is greater than 50%. Be sure to include all of the steps.
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2. [12 pts] For each problem, state which inference procedure you would use to answer the
question, either a confidence interval or hypothesis test and define the parameter (either µ
or p) for the inference procedure in the context of the problem. DO NOT PERFORM
THE ANALYSIS.
(a) [4] In a survey, the Pew Research Foundation found that 33% of respondents obtained
their news from the Internet. With 95% confidence, estimate the proportion of the population that obtained their news from the Internet.
(b) [4] How much do users pay for Internet service? A random sample of 50 Internet users
found that they paid a mean of $20.90 per month with a standard deviation of $2.35.
Estimate, with 95% confidence, the mean amount Internet users pay for service.
(c) [4] A previous study claimed the mean cellulose content of alfalfa hay is 142 mg/g. An
agronomist believes the true value is different form 142 mg/g. To test his belief, he takes
a simple random sample of 15 cuttings from the population and finds the sample mean
cellulose content is 145 mg/g with a sample standard deviation of 3 mg/g. Is this sufficient evidence that the mean cellulose content of alfalfa hay is different than 142 mg/g?
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3. [15 pts] The quality control department for an automobile parts manufacturer regularly tests
new parts to determine if they have been manufactured to the correct specifications. In a
recent test, a critical dimension was measured for a simple random sample of 16 automobile
crankshafts. The sample mean distance for the 16 crankshafts was 224.0019 mm and the
sample standard deviation was 0.00618 mm.
(a) [11] The measurement for this dimension of the crankshaft is supposed to be 224 mm.
Is there evidence that the mean dimension is not 224 mm? Conduct the appropriate
hypothesis test. Make sure you include in your answer the null and alternative hypotheses, test statistic, P-value, decision, and conclusion in the context of the problem. Use
a significance level of α = 0.10.
(b) [4] In order for your test above to be valid, what should be the distribution of the measurements?
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4. [13 pts] A study published in a medical journal reported on the survival times of skin grafts
for burn patients. A sample of eleven burn patients were used in the study. Survival times,
Y (in days) for skin grafts for each patient and summaries are given below.
37
19
57
90
16
22
20
18
61
29
60
The sample standard deviation for these data is s = 24.44.
(a) [3] Compute the average survival time of skin grafts for this sample.
(b) [6] Construct a 98% confidence interval for the mean survival time of skin grafts for
burn patients.
(c) [4] Below is a box plot for the sample of of survival times. Describe the shape of the box
plot. Based on this box plot do you think that the sample was taken from a normally
distributed population? Explain briefly.
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5. [19 pts] ACT English subtest scores are assumed to follow a normal distribution with σ = 6.
A random sample of n=25 high school students whose native language is not English take
the ACT. Their sample average score is 15.
(a) [6] Construct a 80% confidence interval for the population mean English ACT score for
high school students whose native language is not English.
(b) [4] Based on the confidence interval in (a), could the population mean for high school
students whose native language is not English be 18? Explain briefly.
(c) [9] Go through the five steps of testing the hypothesis that the population mean ACT
English subtest score is 18 against an alternative that the population mean is not 18.
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6. [18 pts] For each of the following scenarios give the null and alternative hypotheses, indicate
whether the test statistic is a t- or a z-test statistic, explain why, compute the P-value, make
a decision about the null hypothesis, and explain why you reached that decision.
(a) [9] A psychologist wishes to see if students identified as talented and gifted actually have
a higher mean IQ than the usual value of 100. IQ scores are assumed to be normally
distributed with a population standard deviation of 15. Based on a random sample of
16 talented and gifted students the value of the standardized test statistic is 2.13.
(b) [9] A construction engineer wishes to know the mean strength of concrete slabs made
from a new formulation. She tests the hypothesis that the mean strength for the new
formulation is 400 psi versus the alternative that the mean strength is less than 400 psi.
For a sample of 10 slabs using the new formulation the mean is 374.3 and the standard
deviation is 74. The value of the standardized test statistics is −1.10.
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