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MATH 131
Lab 7
8/11
The goal of this lab is to form confidence intervals and perform hypothesis tests using
quantitative data (V3); to determine an appropriate sample size for a selected error tolerance;
and to form a confidence interval for a certain proportion where the population value is
known.
(2 points)
Part 1: Confidence Intervals for Quantitative Data, V3
A. Using the sample mean and standard deviation from Lab 6, form a 95% confidence
interval for the mean of your population. (See p. 307) Use the method discussed in
class to write the statement. It is not sufficient to write an algebraic inequality. You
must write a statement of the form: “I am 95% confident that the actual mean age
of U.S. Senators is between 54.2 and 60.1.”
You must show your work. Use the computer only to check your work.
B. Repeat A for a 99% confidence interval.
C. State clearly the difference between these two confidence intervals. (Explain which is
wider and why.)
(2 points)
Part 2: Sample Size Determination
A. Based upon your experience with your data, select a “desirable” value for E, the
margin of error. (See p. 310) Choose E to be smaller than the E that you computed in
Part A, above. For example, for a Senator’s mean age, you might choose to estimate to
within 1 year; so E = 1 would be used.
B. Calculate the minimum sample size required to produce results accurate to a 95%
degree of confidence and margin of error, E. Show your calculations; use your
sample standard deviation as an approximation for the population standard deviation.
C. Write your answer in statement form like “With a sample size of at least 89, I will be
95% confident that my sample mean will be within 1 year of the true mean age of the U.S.
Senators.”
(3 points)
Part 3: Hypothesis Testing on the Mean
A. Ask someone familiar with the population for your labs to make a claim about the
mean of your quantitative data, V3. Pose the question very generally, like “Make a
statement about the average age of a U.S. Senator”. This will allow 1 or 2 tailed test. The
respondent’s claim will be the basis for the hypothesized population mean.
B. Test the hypothesis from part A using the P-value method with a level of significance of .05.
Make sure to clearly state a separate decision and conclusion at the end of your test.
C. Test the hypothesis from part A again, this time using the classical method and including a
clear sketch of the rejection region.
D. Do your decisions from parts B and C match? Explain.
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MATH 131
Lab 7
(3 points)
8/11
Part 4: Confidence Interval for a Proportion
A. Consider the experiment of rolling a single six-sided dice. Let p be the population
proportion (classical probability) of rolling a 2. What is the value for p? Explain your
reasoning.

B. p is a sample proportion (empirical probability) of 2’s rolled. Use Minitab
to simulate the experiment of rolling a single die 200 times to find your sample

statistic, p . The directions for Minitab are below. The count next to the roll 2 that you will
see on Minitab is the frequency to use to compute the empirical probability.
Select Calc from the menu bar.
Select Random Data.
Select Integer.
In the dialog box, make these
entries:
Generate 200 rows of data.
Store in column C2.
Minimum value: 1
Maximum value: 6
Click on OK.
Select Stat from the menu bar.
Select Tables.
Select Tally.
Type C2 in the Variable box.
Check Counts.
Click OK.
C. Construct a 99% confidence interval for p, the population probability of rolling a 2.
Show your work, using the value computed in B.
D. Does your confidence interval contain the true value computed in A?
E. If 100 students form such confidence intervals, how many of them would you expect
to have created intervals that contain the true p value? (See figure on p. 309.)
Minitab Directions
For Parts 1 and 3,
Select Stat from the menu bar.
Select Basic Statistics from the subdirectory.
Select 1Z 1-Sample z
For Part 4,
Select Stat from the menu bar.
Select Basic Statistics from the subdirectory.
Select 1P 1-Proportion
Choose to enter (1) the sample size, mean and
standard deviation from Lab 6 by clicking in
Summarized Data or (2) the raw data by
indicating the column in which the data is
located by clicking on Samples in Columns.
Click on Summarized data.
Enter 200 as the number of trials.
Enter the number of 2’s rolled as the number of
events.
Click on Options.
Enter 99 as the Confidence level.
Click on OK twice.
Type in the hypothesized mean given by your
expert as Test Mean.
Click on Options.
Enter the Confidence level : .95 (then .99).
Enter Alternative hypothesis as figured in Part 4.
Click OK.
If you entered your raw data, you may select
some graphs.
Click on Graphs.
Check Individual value plot to see visuals of the
confidence intervals and hypothesis tests.
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