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Stat 401 Lab Activity 7
In this activity we will do Minitab implementation of CIs and testing concerning two
population means and two population proportions.
Part I: Test and CIs for two normal means
Consider Exercises 9.14 and 9.15. Copy the data from
http://www.stat.psu.edu/~mga/401/labs/lab7/uts.data.txt, and paste it in the
first two columns of the Minitab worksheet. Normal probability plots on
both samples indicate that the normality assumption is tenable.
a) For Exercise 9.14 we will assume that the two population variances are the same
and will perform the two-sample t-test, and the corresponding CI :
Stat > Basic Statistics > 2-Sample t > Choose “Samples in different columns”;
Check “Assume equal variances”; Go to “Options” and enter desired choices
OK, OK
b) For Exercise 9.15 we drop the assumption that the two variances are the same and
perform the t-test and corresponding CI by repeating the above sequence of commands
except that now we do not check “Assume equal variances”.
Part II: Large sample test and CIs for two means
Consider Exercise 9.2. Here the sample sizes are large enough, so we do not
require the assumption of normality. Use the commands:
Stat > Basic Statistics > 2-Sample t > Choose “Summarized data”; Enter: 42, 0.49,
and 0.19 for the First sample size, mean, and standard deviation; Enter: 42, 0.36,
and 0.16 for the Second sample size, mean and standard deviation, OK
Minitab does not perform the 2-sample Z test, but the above with the above
commands Minitab calculates the Z statistic, but calls it T-statistic. The
value of the T-statistic can be referred to the normal table, even though with
large sample sizes, the p-value given by Minitab using the t-distribution
should be quite close to the normal distribution p-value.
Part III: Test and CIs for two proportions
Consider Exercise 9.5. Thus, from population 1 we have 330 successes out
of 890 trials and from population 2 we have 170 successes out of 550 trials.
Use the commands:
Stat > Basic Statistics > 2 Proportions > Choose “Summarized data”; Enter the
number of trial and the number of events (successes); Check the “Options”; OK
Part IV: The Mann-Whitney-Wilcoxon rank sum test
Consider Exercise 9.21. Copy the data from
http://www.stat.psu.edu/~mga/401/labs/lab7/cloud.seeding.data.txt, and
paste it in columns 3 and 4. Normal probability plots suggest that the
normality assumption is not tenable for either sample. Moreover, the sample
size is not large enough to apply the CLT. We will use the rank-sum test to
test the hypothesis that seeding makes no difference vs the alternative that it
increases rain. The procedure also gives corresponding nonparametric CIs.
Stat > Nonparametrics > Mann-Whitney > Enter Control for First sample, Seeded
for Second sample; Set Confidence level; Select “less than” for Alternative; OK
Part V: Paired data
Consider Exercise 9.18. Copy the data from
http://www.stat.psu.edu/~mga/401/labs/lab7/turbidity.data.txt, and paste it
in columns 5 and 6.
Stat > Basic Statistics > Paired t > Choose “Samples in columns” and enter the data
columns; Check the “Options”, OK
Part VI: Do Exercises 2, 5, 14, 15, 18, and 21 using the above Minitab
command sequences, and turn it in.