Assignment-
Background to the assignment:
In this assignment you will be investigating pulse rate data collected by a sports science researcher who was interested in the effects of various factors on pulse rates at rest and after a short burst of exercise. The data was collected from 91 undergraduate volunteers as follows: The researcher began by recording the height, weight, gender, smoking habits (i.e. smoker or non-smoker), daily activity level, and resting pulse rate of the volunteers. The researcher then divided the volunteers at random into two groups. The first group ran in place for a minute while the other group stood still. Then, the volunteers in each group recorded their pulse rates once more.
Data:
The data is contained in the Mintab worksheet Assign2016.MTW and contains 8 columns:
|
Column
|
Name
|
Description
|
|
C1
|
Pulse1
|
Resting Pulse
|
|
C2
|
Pulse2
|
Pulse after running or not running
|
|
C3
|
Ran
|
Whether student ran or not ('Yes' or 'No')
|
|
C4
|
Smokes
|
Whether student smokes ('Yes' or 'No')
|
|
C5
|
Gender
|
Gender of student: M or F
|
|
C6
|
Height
|
Student's height in inches
|
|
C7
|
Weight
|
Student's weight in pounds
|
|
C8
|
Activity
|
Daily activity level (Slight, Moderate, or A Lot)
|
The Minitab project file Assign2016.MPJ can be found on the Vision page in the Minitab Assignment folder under Assessment.
Assignment Tasks
Task 1 -
To investigate differences between resting pulse rate for smokers and non-smokers, calculate summary statistics for resting pulse for smokers and non-smokers and produce boxplots for resting pulse for smokers and non-smokers. Comment on these statistics and plots.
Task 2 -
Investigate differences between resting pulse rate for men and women by calculating summary statistics for resting pulse for each group and producing boxplots for resting pulse for each group. Comment on these statistics and plots.
Investigate whether there is a statistically significant difference between the mean resting pulse for men and women by carrying out an appropriate 2-sided t test on the difference in the mean pulse rates for the two groups. Clearly state your hypotheses and the assumptions needed for the test, and interpret the result.
Task 3 -
Produce boxplots of resting pulse split by gender and smoker/non-smoker. Comment on these boxplots.
Split the worksheet by gender and investigate whether there is a statistically significant difference between the mean resting pulse rate for women who smoke and for women who do not smoke by carrying out an appropriate 2-sided t test on the difference in mean pulse rates for the two groups. Again, clearly state your hypotheses and the assumptions needed for the test, and interpret the result.
Task 4 -
Create a new column called Differences containing the difference between pulse after running/not running and resting pulse. These values should be reported in the appendix.
Split the worksheet by whether the student ran or didn't run and produce dotplots of the differences for the runners and the non-runners. Comment on the dotplots.
For the group that didn't run, produce a 95% confidence interval for the mean difference between the first pulse measurement and the second pulse measurement. You should note that 0 is in the confidence interval and interpret this.
For the group that ran, carry out an appropriate 1-sided t-test for the mean difference between the the first pulse measurement and the second pulse measurement. Clearly state your hypotheses and the assumptions of the test, and interpret the result.
For the group that ran, determine a lower 95% confidence interval for the mean difference between the first pulse measurement and the second pulse measurement, and comment on this confidence interval.
Task 5 -
Plot weight against height and comment on the plot.
Use the method of least squares regression to obtain an equation for weight in terms of height.
Use the residuals from the regression to comment on whether the assumptions of the regression model are justified. Support your commentary with appropriate plots.
Briefly comment on any limitations of this model.