Minitab Project: Assignment 2

STAT:2020

Fall 2019

TOPIC: Two-sample t-test

Assigned: Wednesday, Dec. 4, 2019

Due: Wednesday, December 11, 2019

This is the second of two short Minitab projects. Minitab projects are 5% of your total points in the class.

Assignment 1 was worth 2% and Assignment 2 is worth 3%.

This assignment is meant to give you some experience using Minitab for a two-sample t-test. The data set is

called ‘cholesterol.xlsx’ and can be downloaded at our website:

http://homepage.stat.uiowa.edu/~rdecook/stat2020/minitab.html

Information on getting started in MINITAB and incorporating your data is shown on Assignment 1 project

description (the link is still up). This data set is not a .csv file, but is rather a .xlsx file, so when bringing in the

data, use the following…

From the pull-down menu: File à Open worksheet… Then under `Files of type’ choose ‘Excel (*.xls,*.xlsx)’

and then click on your data file. Your data should appear in the Worksheet Window in Minitab.

The data set:

A study was conducted at a major northeastern American medical center regarding blood cholesterol levels and

heart-attack incidents. A total of 28 heart-attack patients had their cholesterol levels measured after the attack.

In addition, cholesterol levels were recorded for a control group of 30 people who had not had a heart attack.

The two groups were independent of each other.

Variables – descriptions (check that your data looks like this):

patient – Patients numbered 1 to 58.

group – Group 1 = heart attack group and Group 2 = control group.

cholest – Cholesterol is the measured response in mg/dL of blood.

The researchers were interested in comparing the mean level of cholesterol between patients who have had a

heart attack and patients who have not had a heart attack. We will use Minitab to perform the relevant

hypothesis test at the α=0.05 level.

H

0 :µ1 = µ2

H

1 :µ1 ≠ µ2

Questions/comments in bold are to be answered and turned-in with the other output.

1) Compare the center and spread of the distributions of cholesterol values for the two groups using side-byside boxplots (see the instructions below).

Use the pull-down menu: Graph à Boxplot…

Under ‘One Y’ highlight ‘With Groups’ then press OK.

You should now see a dialog box called ‘Boxplot – One Y, With Groups’. Next we need to tell Minitab

which variable is the response variable (cholest) and which variable is the grouping variable (group) for

the side-by-side plots.

In the dialog box, place your cursor in the ‘Graph variables’ box, then highlight ‘C3 cholest’ and press Select

(you should see cholest appear at the right in the top box).

In the dialog box, place your cursor in the ‘Categorical variables for grouping’ box, then highlight ‘C2 group’

and press Select (you should see group appear at the right).

After cholest appears in the top box and group appears in the lower box, press OK.

Copy and paste the boxplot into your Word document*(see footnote at end). Under the plot, briefly

compare and contrast the center (median) and spread of the two distributions.

2) Generate the cholesterol statistics (mean, median, standard deviation, etc.) and histogram separately for

each group (see the instructions below).

Use the pull-down menu: Stat à Basic statistics à Graphical summary…

In the dialog box, place your cursor in the ‘Variables:’ box, then highlight ‘C3 cholest’ and press Select

(you should see cholest appear at the right in the top box).

In the dialog box, place your cursor in the ‘By variables:’ box, then highlight ‘C2 group’ and press Select

(you should see group appear at the right in the lower box).

After cholest appears in the top box and group appears in the lower box, press OK.

You should now see a summary window for each group.

Copy and paste BOTH summary windows into your Word document.

Under the pasted output, number and do the following:

1. Using the summary information Minitab has generated, calculate and provide the IQR for each group.

2. Based on the output you have produced so far, state why it may be more appropriate to perform a twosample t-test assuming σ12 ≠σ 22 rather than σ12 = σ 22 (state specific values from output for full credit).

3. Briefly comment (in the context of the data and research question) on which group seems to have higher

cholesterol values and how this relates to the research question at hand.

3) Perform a two-sample t-test assuming case 2: σ12 ≠σ 22 (see instructions below).

Use the pull-down menu: Stat à Basic statistics à 2-Sample t…

In the ‘Two-sample t for the Mean’ dialog box, you should see ‘Both samples are in the same column’

(and this is the appropriate choice for this data file).

Place your cursor in the ‘Samples:’ box, then highlight ‘C3 cholest’ and press Select

(you should see cholest appear at the right in the top box).

In the dialog box, place your cursor in the ‘Sample IDs:’ box, then highlight ‘C2 group’ and press Select

(you should see group appear at the right in the lower box).

Click on the ‘Options’ button. Make sure the ‘Assume equal variances’ box is NOT checked and press OK

on the ‘Two-Sample t: Options’ dialog box.

Press OK in the ‘Two-sample t for the Mean’ dialog box.

Copy and paste the results of the ‘Two-Sample T-Test and CI: cholest, group’ appearing in the `Session’

window into a Word document.

Under the output, number and answer the following questions:

1. What were the degrees of freedom for the t-test statistic?

2. Why were the degrees of freedom not equal to n1 + n2 – 2?

3. What was the mean cholesterol for each sample group?

4. What was the value of the test statistic?

5. What was the p-value? (provide up to 3 decimal places)

6. What was the decision in the hypothesis test? Reject the null or not?

7. Did Minitab provide the difference as “control – heart attack” or as

“heart attack – control”? (This affects interpretation of the values).

8. Provide the 95% confidence interval for the difference in the population means (i.e. for µ1 –µ2 )

9. The 95% confidence interval for the difference in the population means does NOT include

zero… what relevant information does this give us with respect to the hypothesis test of interest?

*If you are having trouble directly copying and pasting any graphics from Minitab into Word, another option is to first

save the graphic to a file and then insert it into your Word document later. To do this, highlight the graph of interest in

Minitab, then: File à Save graph as… Save as type (*.JPG) and put it into a folder. While in Word, choose: Insert à

Photo… à Picture from File.

NOTE: Please fit all your responses into a 2-page document (front and back preferred). You can re-size graphics as

needed and answers need to only be brief (just answer the question at hand).

Source

Ryan, B. F., Joiner, B. L., and Ryan Jr, T. A. (1985). Minitab Handbook Second Edition. Duxbury Press, Boston.

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