Spring 2011 Hypothesis Testing II with Small Samples
2/10/2016 5:06:54 AM
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First Name
Student 1
Student 2
Student 3
Student 4
Student 5
Score
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Team #
Objectives
By the end of this activity you should be able to
 Explain when to use the student t-distribution and when to use the normal distribution in
conducting hypotheses tests for the population mean
 Accurately conduct hypothesis tests using the t-distribution
1) A random sample of size 16 is taken from a normal population whose standard deviation
equal to 10. The sample mean is found to be 24.2 and the sample standard deviation is 9.7.
The actual population mean is believed to be 20.
a) Explain why you should use a normal distribution rather than a t-distribution to test the
hypothesis that the mean is 20 versus mean is greater than 20 in this case.
20 points
b) State the null and alternative hypothesis for the test, report the p-value of your test and
your conclusion at the 95% significance level.
c) Now suppose that the sample results are the same, but that the population standard
deviation is unknown. State the null and alternative hypothesis for the test, report the pvalue of your test and your conclusion at the 95% significance level.
d) Lastly, explain why the p-value in part c) is larger than that in part b) even though the
sample standard deviation is smaller than the actual population standard deviation.
2) A sample of 19 cigarettes of a certain brand was tested for nicotine content and gave a
sample mean of 22 and a sample standard deviation of 3.5 milligrams. Perform a hypothesis
test to see if the mean nicotine content of this brand of cigarettes is higher than 20.
a) State the null hypothesis H0:
b) State the alternative hypothesis HA:
.
Spring 2011 Hypothesis Testing II with Small Samples
2/10/2016 5:06:54 AM
c) Conduct a hypothesis test and report the p-value for this test.
.
.
d) Interpret the results of you test at the 90%, 95%, and 99% significance levels.
20 points
3) Suppose a random sample of 10 loaves of bread is selected from a local bakery’s output.
Suppose that the mean weight and the standard deviation of these 10 loaves are 15.8 ounces
and 0.4 ounce, respectively. Perform a hypothesis test to see if the average weight of the
bread from this bakery is less than one pound (16 ounces).
a) State the null hypothesis H0:
20 points
b) State the alternative hypothesis HA:
.
c) Conduct a hypothesis test and report the p-value for this test.
.
.
d) Interpret the results of you test at the 90%, 95%, and 99% significance levels.
4) Researchers are experimenting with a new compound used to bond Teflon™ to steel. The
compounds currently in use require an average drying time of three minutes. It is thought
that the new compound dries in a shorter length of time.
When the experiment is conducted, these data are obtained:
1.4
2.1
2.8
0.9
2.4
1.7
3.7
2.7
2.6
1.9
2.8
2.8
2.2
2.2
3.4
1.9
a) Compute the sample average drying time and standard deviation for the new compound.
25 points
Spring 2011 Hypothesis Testing II with Small Samples
2/10/2016 5:06:54 AM
b) We wish to conduct a hypothesis test to see if the new compound dries faster. State the
null hypothesis H0:
c) State the alternative hypothesis HA:
.
d) Conduct a hypothesis test and report the p-value for this test.
.
.
e) Interpret the results of you test at the 90%, 95%, and 99% significance levels.
5) A sleep-producing drug was administered to 10 patients and produced a mean increase in
sleep of 12 minutes. If the standard deviation for the 10 patients was 18 minutes, conduct a
hypothesis test to see if the drug does increase sleep time.
a) State the null hypothesis H0:
20 points
b) State the alternative hypothesis HA:
.
c) Conduct a hypothesis test and report the p-value for this test.
.
.
d) Interpret the results of you test at the 90%, 95%, and 99% significance levels.
6) Consider the preceding problem but suppose that the sample size was 50 rather than 10. The
null and alternative hypotheses are the same.
a) Conduct the hypothesis test and report the p-value for this test.
.
15 points
Spring 2011 Hypothesis Testing II with Small Samples
2/10/2016 5:06:54 AM
.
b) Interpret the results of you test at the 90%, 95%, and 99% significance levels.
c) Explain in detail why the p-values obtained in questions 5 and 6 are different and
interpret the meaning in the context of the problem.