KINS 2206: Normal Distribution, Sampling Methods & Design of Experiments - Accounting Assignment Help

Assignment Task:

The questions in this assignment are to be done without the use of R  Commander. 

1. [15 marks] There are 6 school buses that pass by Langara College every morning at 8am. Each of  these school buses has the following number of students (i.e. riders): 27, 51, 55, 32, 37, 38. a) Describe, in words, each of the following, in the context of the data: individual (i.e. observation),  variable, and what type of variable is this (categorical or quantitative). [3 marks] b) Calculate the mean, standard deviation and the five-number summary of these data. Show your  work. [6 marks] 

c) Interpret, in the context of the data, the mean and standard deviation from part b). [3 marks] d) Are there any outliers in this dataset? (Remember to use the rule for outliers here!) Show your  calculations and make an appropriate conclusion. [3 marks] 

2. [4 marks] It appears that people who are mildly obese are less active than leaner people. One study  looked at the average number of minutes per day that people spend standing or walking. Among mildly  obese people, minutes of activity varied according to the N(373, 67) distribution. Minutes of activity for  lean people had the N(526, 107) distribution. Within what limits do the active minutes for about 95%  of the people in each group fall? Use the 68-95-99.7 rule.  

3. [2 marks] The heights of people for the same sex and similar ages follow a Normal distribution  reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of women  aged 20 – 29 in the United States have mean 161.9 pounds and median 149.4 pounds. The first and  third quartiles are 126.3 pounds and 181.2 pounds, respectively. What can you say about the shape of  the weight distribution? Why?  

4. [4 marks] The return on a stock is the change in its market price plus any dividend payments made.  Total return is usually expressed as a percent of the beginning price. Excluding the three low outliers,  the average return of the remaining 369 months is 0.84% with a standard deviation of 4.097%. If the  distribution of the 369 months (excluding the outliers) were exactly N(0.84, 4.097), what would be the  proportion of months with returns greater than: a) 0%; b) 4%?  

5. [5 marks] A pacemaker is a medical device that uses electrical impulses, delivered by electrodes contracting the heart muscles, to regulate the beating of the heart. Pacemaker implantation is a  necessary treatment for patients who suffer from severe bradycardia (a condition where resting heart  rate is less than 40 beats per minute (BPM), which is considered abnormal). A cardiac surgeon at St.  Paul’s Hospital in Vancouver was conducting research on survival times (i.e. time from a patient’s  pacemaker surgery until his/her death) from 6505 patients who were implanted a pacemaker between 

the years 2001 and 2013. The surgeon has found that the survival times (measured in months) follow  approximately a normal distribution with mean 101.9 months and standard deviation of 34 months. a) What percentage of patients survived between 75 and 90 months? [3 marks] b) Patients with a survival time in the top 20% require pacemaker replacement. What survival time must  a patient reach in order to have a pacemaker replacement? [2 marks] 

6. [2 marks] A study in El Paso, Texas, looked at seat belt use by drivers. Drivers were observed at  randomly chosen grocery stores. After they left their cars, they were invited to answer questions that  included questions about seat belt use. In all, 75% of drivers said they always used seat belts, yet only  61.5% were wearing seat belts when they pulled into the store parking lots. Very briefly (in 1 to 2  sentences only!) explain the reason for the bias observed in responses to the survey. And indicate what  type of bias i.e. non-sampling error is this. 

7. [4 marks] The 10th Annual Health Care in Canada Survey is a survey of the Canadian public’s and health  care providers’ opinions on a variety of health care issues, including quality of health care, access to  health care, health and the environment, and so forth. A description of the survey follows: The 10th edition of the Health Care in Canada Survey was conducted by POLLARA Research between  October 3rd and November 8th, 2007. Results for the survey collected using a random sampling method  are based on telephone interviews with nationally representative samples of 1,223 members of the  Canadian public, 202 doctors, 201 nurses, 202 pharmacists and 201 health managers. Public results are  considered to be accurate within +/-2.8%, while the margin of error for results for doctors, nurses,  pharmacists and managers is +/-6.9%. Note the margin of error is a sampling error (which is one of the  sources of error that is a part of any sampling method).  

a) Why is the accuracy greater for the Canadian public than for health care providers and managers? [2  marks] 

b) Why do you think they sampled the public as well as health care providers and managers? [2 marks] 

8. [6 marks] Observational studies have suggested that daily intake of magnesium supplement is  associated with a lower blood pressure. Yet, carefully designed double-blind, randomized experiments  (where placebo was used in a control group) have shown that magnesium has no effect in reducing blood  pressure.  

a) For each study (observational and experiment), what are the response and explanatory variables and  treatments? [2 marks] 

b) Outline the design of each study on a diagram [2 marks] 

c) For the observational study, identify a confounding variable that may explain the association between  magnesium supplement intake and lower blood pressure? Explain why your answer satisfies the  definition of a confounding variable. (Hint: What can you say about people who regularly take  magnesium supplements?) [2 marks]

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