Reference no: EM133120820

STA8170 Statistics for Quantitative Researchers - University of Southern Queensland

Question 1

This question uses information from the data file cardiac_22.sav found under the Assessment block on the StudyDesk (also see cardiac_22.txt for more details about the study and the variables measured). Make sure the Variable View in SPSS is setup properly with all ‘labels' correctly defined (with units), all ‘values' assigned correctly for categorical variables and the correct ‘measure' selected for all variables.

Use SPSS to find the answers to the following questions, but do not copy and paste SPSS output into your answer for parts (c) and (d) (make sure you always include units where appropriate).

(a) Display the distribution of ‘height' of patients in the study using an appropriate graph. Label the axes correctly, include units of measure and provide an appropriate title. Include your name in the title of the graph.

(b) Using the graph produced in part (a) only (don't refer to SPSS summary statistics), describe in no more than 60 words, the distribution of ‘height' of the patients in this study. Include comments on shape, centre and spread of the distribution and the existence of outliers, if any. Do not perform any calculations; use the graph only.

(c) What is the sample size, mean and standard deviation of the distribution of ‘height' of the patients, in this study? (You can use SPSS to calculate them but do not copy/paste SPSS output).

(d) Using SPSS find the median, first quartile, third quartile and IQR of the distribution of ‘height' of patients in this study. (Do not copy/paste SPSS output).

(e) For the distribution of ‘height' of patients, which statistics are appropriate to measure its centre and spread? Give a reasonable explanation for your choice.

(f) Using an appropriate graph compare the distribution of cardiac index of the male and female patients, and explain the key differences of the two distributions.

Question 2

Use this extract taken from the article, "Cranberry Juice Can Effectively Reduce Heart Disease," (appeared on preventdisease.com on January 1, 2019) to answer the questions that follow:

Researchers from the University of Scranton suggested that nutrients found in cranberry juice can effectively reduce the risk of heart disease -- in some cases, up to 40 percent -- mostly by increasing levels of HDL, the "good" cholesterol. The juice was also shown to increase blood levels of antioxidant nutrients by up to 121 percent.

The research involved 11 women and 8 men, all diagnosed with high cholesterol (on average 250 milligrams per deciliter), and none were taking any cholesterol medication. Normal cholesterol is below 200 mg/dl.

Ten of the participants were assigned to drink cranberry juice containing an artificial sweetener and no added sugar, while the remaining nine drank juice sweetened with corn syrup. All the drinks contained 27 percent fruit juice, the average amount commonly found in many grocery store brands.

During the first month of the 90-day trial, each volunteer drank one daily eight-ounce serving of juice. The second month they consumed two glasses a day, and the third month three glasses daily. At the conclusion of each of the three months, researchers measured participants' total cholesterol, their HDL, and their triglycerides. They also measured levels of antioxidants -- nutrients that protect our heart by blocking certain types of cell damage caused by molecules generated by smoking and pesticide exposure.

"After one month there was no change in any of the participants. At two servings a day, triglyceride levels rose marginally, but only in those drinking sweetened cranberry juice,"

However, once intake rose to two glasses daily, antioxidant levels also rose by 111 percent; when three glasses a day were consumed, researchers reports it climbed to a whopping 121 percent in both types of juices. What's more, the HDL or "good" cholesterol of those drinking three glasses of either juice per day jumped up by 10 percent. "That's equal to approximately a 40 percent reduction in heart disease".

Researchers note that the study was not a controlled trial and there was virtually no attention paid to any changes in the participants' diet or exercise regimens. Moreover, they were not questioned as to any lifestyle or other changes that could have affected the study outcome.

(a) Is this an experimental or observational study? In less than 50 words clearly explain your choice based on the extract given above.

(b) For the above study identify, if appropriate, the
i) response variable(s).
ii) factor and its levels.
iii) sample size.

(c) Are the four principles of experimental design used in this study? Explain, in the context of the study.

(d) Explain explicitly what a confounding variable is. Identify one plausible confounding variable in this study and explain why it is a confounding variable.

Question 3

A study on the resting heart rates of marathon runners found that their resting heart rates are normally distributed with mean of 58 bpm and a standard deviation of 5 bpm (where bpm = beats per minute). A resting heart rate of 64 bpm is considered very high for a marathon runner. Use this information to answer the questions below:

(a) Identify the variable of interest and the unit of measurement of the variable of interest here.

(b) Based on the distribution of resting heart rates of marathon runner, what percentage of marathon runners have a high resting heart rate (i.e., exceed 64 bpm)?

(c) Based on this distribution, what percentage of marathon runners have a resting heart rate between 55 bpm and 65 bpm?

(d) From previous records it has been shown that 2% of marathon runners are considered to have a dangerously low resting heart rate. Below what resting heart rate do these marathon runners have?

(e) For a random sample of 25, what is the probability that the mean heart rate of marathon runners will under 55 bpm?

Question 4

Consider the data in the file cardiac_22.sav again. This time we are interested to see if there is a relationship between cardiac index and hemoglobin level for patients who did not survive cardiac arrest after being admitted to hospital. Before commencing this problem, you ?rst need to select only those patients who did not survive cardiac arrest (see Selecting Cases recordings under SPSS Resources in the StudyDesk for help on how to do this).

(a) What are the two variables the researcher will need to include in the analysis? What type of variables are they?

(b) Use an appropriate graph to display the relationship between the two variables identified in part (a). Label the axes correctly, include units of measure and provide an appropriate title. Include your name in the title of the graph.

(c) From the graph in part (b), describe (in no more than 30 words) the form, direction, and scatter of this relationship, and identify any outliers.

(d) Calculate an appropriate statistic to measure the strength and direction of the relationship between the two variables for patients who did not survive cardiac arrest after being admitted to hospital. Justify your choice of this statistic and interpret what it tells you about the relationship.

(e) Use SPSS output to write the equation of the regression line which could be used to predict cardiac index from hemoglobin level for patients who did not survive cardiac arrest after being admitted to hospital and then plot the regression line on the graph in part (b).

(f) Using the regression equation from part (e), predict the expected cardiac index of a patient whose hemoglobin level is 112 g/100mL. Would you consider this to be an accurate prediction? Why or why not?

(g) What proportion of the variability in cardiac index of patients who did not survive cardiac arrest after being admitted to hospital has been explained by the model?

Question 5

A doctor knows from experience that 5% of patients who are prescribed a certain drug will experience undesirable side e?ects. A randomly selected group of 11 patients have been prescribed this drug. A particular variable of interest is the ‘number of patients who experience undesirable side effects'. Based on the above information answer the following questions:

(a) What is an appropriate model to represent the variable of interest? Write down the parameters of the model, if any.

(b) Discuss, in context, how the conditions of the appropriate model in part (a) are satisfied.

(c) Using the parameters of the model find the mean and standard deviation of the number of patients who experience undesirable side effects.

(d) Find the probability that no more than three of these 11 patients will experience undesirable side effects.

(e) Determine the probability that, in a random sample of 500 patients who have been prescribed this drug, 40 or less will experience undesirable side effects. State and check any assumptions, conditions or rules of thumb that should be considered before performing the calculations to determine this probability.

Attachment:- Statistics for Quantitative Researchers.rar