Statistics: Lab #4
Chapters 9 - 10
You will have two files for this lab, they are separated
below as parts A and B.
PART A, Hypothesis Tests (1
population)
Hypothesis
testing one population.
Data: We
will be using some data from the Fall 2015 Student Database
to conduct hypothesis tests.
Preparing the data: Start a new file, put your name(s) in cell
A1 and today’s date in A2, and then copy the Female, and Alcohol columns of
data from the database into columns B and C.
Now copy the Greek column and Donate column of data into that worksheet
and save it as Stat Lab 4 TESTS, yourname. This will
serve as your sample of college students. Remember a woman is labeled with a 1
and a man is labeled with a 0. A student who says they will donate money back
to the college is labeled with a 1, a student who has
not is given a 0. A student in a Greek organization is identified with a 1, and
a student who is not is given a 0. The Alcohol column is the number of alcoholic
drinks the student claims to consume in a typical week.
Note: In your separate lab report, set up and
solve each of the following three problems, submitting with your lab. Do
not delete observations that have missing data. You may assume that you are
sampling from an infinite population.
1. You will need to create a table of descriptive
statistics for all four variables so that you know the sample mean, sample
standard deviation and the number of responses. Put this output at the top of
the worksheet. (4 points)
2a. Using the techniques covered in class,
conduct a hypothesis test, including both a test statistic and a p-value
that tests this research question: Is the average drinking of Hanover College
students significantly greater than 3 drinks per week? Show all of your work in
your lab report, including the null and alternative hypotheses, and be sure to
specify a level of confidence. Thoroughly explain your results. (4 points)
2b. Now we’ll do this using the Ztest
formula in Excel. The output of the Z-test is the p-value of the hypothesis
test that a sample mean is greater than a hypothesized population mean. Somewhere
near the descriptive statistics, create a label called Test 1. In the cell
below this label type =ztest and then click on the
function key ƒx . A window opens and you need to input the range of the alcohol data, the hypothesized population mean
and, if it is known, the population standard deviation. If this last part is
left blank, Excel will substitute the sample standard deviation so you can
leave it blank. Using the result produced by the formula, thoroughly explain
the results of this hypothesis test. (3 points)
3a. Using the techniques covered in class,
conduct a hypothesis test, including both a test statistic and a p-value
that tests this research question: is the population proportion of students at
Hanover College who are in a Greek organization less than .50? Show all of your
work, including the null and alternative hypotheses, and be sure to specify a
level of confidence. Thoroughly explain your results. (4 points)
3b. Now repeat this
test using the Ztest formula in Excel. Create a label
called Test 2. Put the Ztest formula in below this
label. You may need to modify the output of the test to compute the accurate
p-value. Using the result produced by the formula, thoroughly explain the
results of this hypothesis test. (3 points)
4a. Using the techniques covered in class,
conduct a hypothesis test, including both a test statistic and a p-value
that tests this research question: is the population proportion of students at
Hanover College who plan to donate back to the college different from .50? Show
all of your work, including the null and alternative hypotheses, and be sure to
specify a level of confidence. Thoroughly explain your results. (4 points)
4b. Now repeat this
test using the Ztest formula in Excel. Create a label
called Test 3. Put the Ztest formula below the label.
You may need to modify the output of the test to compute the accurate p-value.
Using the result produced by the formula, thoroughly explain the results of
this hypothesis test. (3 points)
Part B: Hypothesis testing two
populations.
Sort the Data: We would like to do some hypothesis
tests comparing women and men and Greek and non-Greek students.
Copy the Greek and Alcohol columns of data
and re-paste them in a second worksheet in the same Excel file. Click at the
top of the Greek column and click on the button that says Sort and Filter. Select largest to smallest (Z to A). You
should now see all of the data from the Greek students (Greek=1) arranged from
the top of the spreadsheet down to the first non-Greek student (Greek =0).
For the Alcohol data, do descriptive
statistics so that you have the separate means, variances and number of
observations for both the Greek and non-Greek students. Clearly label these
somewhere near the top of the worksheet. We will assume that the sample
variances are equal to the known population variances. (2 points)
1a. Do Hanover Greek students drink
significantly more in a week than Hanover non-Greek students? In your separate
lab report, conduct a hypothesis test, including both a test statistic and a
p-value that tests this research question. Show all of your work and be sure to
specify a level of confidence. Thoroughly explain your results. (4 points)
1b. Now use Excel to conduct the very same hypothesis test. In the Data Analysis menu, choose “z-test: two sample for means”. Variable 1 range is your range of Greek drinking. Don’t check the Labels box. The variable 2 range is the range of non-Greek drinking. The hypothesized mean difference is zero. Enter the variance for each from the formulas you created earlier. Select the same level of alpha that you used when you did this by hand. Select a location for the output. (4 points)
1c. Using the result produced by Excel, thoroughly explain the outcome of this hypothesis test. What can you conclude about the mean drinking between Greek and non-Greek students? Be as specific as possible. (3 points)
Now copy and re-paste the Female and Donate columns in a third worksheet in the same Excel file. Sort the Female column so that we see all of the female students at the top, followed by the male students and their corresponding decision to donate. We will assume that the Female students are population 1.
For the Donate data, do descriptive statistics so that you have the separate sample proportions and number of observations for both the female and male students. Clearly label these somewhere near the top of the worksheet. (2 points)
2a. Is there a difference between the proportion of female and male students that plan to donate back to HC? In your lab report, conduct a hypothesis test, including both a test statistic and a p-value, which tests this research question. Be sure to use the appropriate techniques for this situation. Show all of your work and be sure to specify a level of confidence. Thoroughly explain your results. (4 points)
2b. Now use Excel to conduct the very same hypothesis test. This time choose the “t-test: Two Sample Assuming Unequal Variances” form of the test. Using the result produced by Excel, thoroughly explain the results of this hypothesis test. What can you conclude about the proportion that plan to donate between these two groups of students? Be as specific as possible. (4 points)
3. For either of the two tests above, would your conclusions have changed if you selected different values for alpha? Explain and please be specific. (2 points)
Save
your file.
OK, you’ve carefully completed both parts A and B to this lab. You’ve
double-checked that you have all printouts and your typed responses to
questions. Bring printouts and typed comments to class on the due date. Your
emailed files must also be sent by the beginning of class on the due date. When
you email your file, make sure your name is in the filename. Late assignments
or those sent incorrectly will be penalized. Check the syllabus or ask for help
if you’re uncertain of how to do any of this.