It is generally believed that one of the negative effects of quit smoking is weight gain. To examine this issue a group of ex-smokers who had quit 12 months earlier was asked to report their weight gain. Draw at least two appropriate graphs, calculate relevant descriptive statistics and describe what the graphs and statistics tell you. (Data can be found in ‘Assignment 1 data .xls’). Use the statistical package for graphs and descriptive statistics. Copy your output in your answer report. Use 8 classes for histogram. (1+0.5+1= 2.5 marks)
Question 2 Laser surgery to fix short-sightedness is becoming more popular. However, for some people, a second procedure is necessary. The following table lists the joint probability of needing a second procedure and whether the patient has a corrective lens with a factor (dioptre) of minus 8 or less. Use formula.
Vision corrective factor > -8 Vision corrective factor -8
First procedure is successful
Second procedure is required
a) Find the probability that a second procedure is required. b) Determine the probability that someone whose corrective lens factor is minus 8 or less does not require a second procedure. c) Are the events independent? Explain your answer.
(0.5+0.5+0.5 = 1.5 marks)
Question 3 The number of magazine subscriptions per household is represented by the following probability distribution.
Magazine subscriptions per household 0 1 2 3 4
Probability 0.48 0.35 0.08 0.05 0.04
a) Calculate the mean number of magazine subscriptions per household. b) Find the standard deviation. c) If all magazine subscriptions cost $60 per year and all households charged a flat $70 per year for a TV licence, how much would you expect the average household to pay in total for magazine subscriptions and their TV license? Use formula.
(0.5+0.5+1= 2 marks)
Question 4 The head of a business school claims that the average MBA graduate is offered a starting salary of $55,000. The standard deviation of the offers is $4,600. Use both the package and (formula with the statistical tables) to answer the following questions. a) What is the probability that in a random sample of 38 MBA graduates, the mean starting salary is less than $53,000? b) What if only 16 students had been sampled?
((0.5+0.5)+(0.5+0.5)=2 mark) Question 5 A certain type of automobile battery is known to have a lifetime, which is normally distributed with mean 1100 days and standard deviation 80 days. If the manufacturer selects two batteries randomly, what is the mean and the standard deviation of the random variable defined as the difference between the life times of the two batteries (Hint: treat each battery as an independent random variable). Use formula only. (0.5+0.5=1 mark)
Question 6 The number of cars sold annually by used car salespeople is normally distributed. Use both the package and (formula with the statistical tables)) to answer parts a, b and c. a) Find the 95% confidence interval for mean given a sample of 10 salespeople has a mean of 75. The population standard deviation is known to be 15. b) Find the 95% confidence interval for mean given a sample of 400 salespeople has a mean of 75 and standard deviation of 15. c) Assume the mean and the standard deviation of cars sold annually are both unknown. Find the 95% confidence interval given a sample of 10 salespeople has a mean of 75 and standard deviation of 15. d) Compare the width of the confidence intervals in (a), (b) and (c). If they are different, give reasons why they are different. e) How large a sample (given σ = 15) would need to be to ensure that the 99% confidence interval for the mean number of cars sold annually contains the maximum error of 10? ((0.5+0.5)+(0.5+0.5)+(o.5+0.5)+0.5+0.5= 4 marks) Question 7 Twelve university students enrolled in a statistics course were randomly selected. At the competition of the course they were asked how many hours they spent doing homework. It was recommended that they spend three hours per week studying for the duration of the twelve week course. Construct a test to determine whether there is evidence that the average student spent less than the recommended time studying. Write your null and alternative hypotheses clearly. Data can be found on ‘Assignment 1 data .xls’. Use both the package and (formula with the statistical tables)) to answer this question.
Question 8 In assessing radio advertisements, sponsors consider not only the total number of listeners, but also their ages. The 18-34 age group is considered to spend the most time listening. To examine the difference in listening habits between 18-34 and 35-50 age groups a survey of 250 people from each group was conducted, measuring the number of minutes spent listening to radio per day. Data can be found on ‘Assignment 1 data .xls’. Use the statistical package only to answer the following questions. a) Can we conclude that a difference exists between the two groups? Write done your hypotheses clearly. Explain your reason. Use 5% significant level. b) Estimate with 95% confidence interval of the difference between the means of the two groups. c) Does your confidence interval (in part b) confirm your conclusion in part (a)? Explain your reason. ((0.5+0.5)+(0.5+0.5)+0.5= 2.5 marks)
Question 9 As part of a study to investigate the relationship between stress among corporate executives and a measure of the size of the corporation size they work in, the following data were collected on a simple random sample of fifteen corporate executives. Data can be found on ‘Assignment 1 data .xls’. Use the statistical package only to answer the following questions.
(a) Write down the regression model for the problem. Provide sample estimates for the unknown parameters, gradient and intercept in your model. (b) Predict the stress level for the corporate executive who is working in a Corporation that has 730 employees. (c) Is the fitted model suitable for the prediction of stress level? Provide a reason for your answer. (d) Test the hypothesis that there exist a regression model between Y and X. Write down your null and alternative hypothesis. Use the package output to state your conclusion.