24 JULY 2016
MATH 311- LAB 4
ONE-SAMPLE HYPOTHESIS TESTING AND
CONFIDENCE INTERVALS FOR MEANS
DUE: TUESDAY, APRIL 29TH AT 3:00 P.M.
In this lab, you will work with descriptive statistics, one-sample hypothesis testing, and
one-sample confidence intervals.
Objectives:
By the end of the laboratory, you will be able to
 Use Minitab to calculate descriptive statistics and interpret the output
 Perform one-sample hypothesis testing using Minitab.
 Calculate a one-sample confidence interval using Minitab and interpret the output.
Scenario:
The average number of children that a woman in the United States will have during her
lifetime was recently reported to be 2.0 by the CDC (Center for Disease Control).
A certain professor, however, believes that families which have children in college are, in
general, larger than the “average” American family. Thus, a simple random sample of 51
students from a university was asked “How many children did your mother have?” The
results are tallied below:
Number of Children
2
3
2
2
8
2
2
3
4
1
2
2
3
2
2
1
3
2
5
4
3
2
3
3
4
2
2
3
2
2
1
2
3
3
3
3
2
2
2
2
3
3
3
3
2
3
4
4
2
2
3
Question 1: The distribution of the average number of children mothers have should be
normal. Draw a picture of a normal curve below. No, I’m not joking. The mean, median,
and mode of this picture should be 2.0 according to the scenario.
Question 2: The professor will do a 1-sample hypothesis test on these data. Identify,
using a correct English sentence, exactly who the population being tested is.
Question 3: Formulate the null and alternative hypotheses we’ll use to test the
professor’s belief. Clearly define the parameter being tested (i.e. state what μ represents).
Let μ =
H0: μ =
HA: μ
Now enter the data above into a Minitab worksheet. Label the column “Children.”
Question 4: Run the descriptive statistics on the number of children in our sample. Fill
in the blanks below:
n = __________
sample mean = __________
sample median = __________
sample standard deviation = __________
Note: because our sample is relatively large, it’s not unreasonable to assume that the
standard deviation of our sample (found above) is approximately equal to the standard
deviation of our population. Thus in the calculations that follow, use our sample’s
standard deviation as the population’s standard deviation.
Question 5: Perform a 1-sample z-test on Minitab. The steps are below, if you need
them.
z-test statistic = __________





p-value = __________
Go to STAT>BASIC STATISTICS>1-SAMPLE Z.
Select Children to put in the Variables box.
Type the standard deviation from Question 4 in the Standard Deviation box.
Click Perform hypothesis test and type 2.0 in the Hypothesized mean: box.
Click Options and under Alternative choose the appropriate option (“ not equal
to,” “less than,” etc.).
 Click OK.
Question 6: Interpret the results of the test. Note: when using the Z test, if the observed
significance level (p-value) is less than the chosen significance level (typically 5%), then
we reject the null hypothesis and accept the alternative. Otherwise we do not reject the
null hypothesis. We never “accept the ‘null.’”
Question 7: Compute a 1-sample confidence interval with a 90% confidence level.
The steps are listed below if needed.
90% Confidence Interval:




Go to STAT>BASIC STATISTICS>1-SAMPLE Z.
Select Children to put in the Variables box.
Click Options and type 90.0 in the Confidence level box.
Click OK twice.
Question 8: Now compute 95% and 99% confidence intervals:
95% Confidence Interval:
99% Confidence Interval:
Question 9: Which of the three confidence intervals you just computed had the largest
margin of error?
And now for something not completely different….
Radon is an odorless gas that may concentrate in tightly closed houses. Because it’s
slightly radioactive, there is some concern that it may be a health hazard. Researchers
bought 12 radon detectors and tested their accuracy. Each detector was exposed to a
known concentration of 105pCi/l of radon for 3 days and the readings for each is
compiled in the worksheet Radon.mtw. Let μ be the average reading from this
concentration in the population of all detectors of this type.
We would like to test whether the detectors are accurate.
Question 10: What hypotheses should be tested?
H0: μ = _______
HA: μ ________
Open the data set Radon.mtw and perform the appropriate test.
Assume, somewhat unrealistically, that σ is known to be 9.
Question 11: Complete the following:
z-test statistic = __________
p-value = __________
Question 12: What should we conclude? Use a 5% significance level.