The questions to be answered are: Question 1 (7 marks) (Note this question is from the Week 4 Tutorial) Assume you are going to estimate a linear regression based on the following data. Advertising...

The questions to be answered are: Question 1 (7 marks) (Note this question is from the Week 4 Tutorial) Assume you are going to estimate a linear regression based on the following data. Advertising Expenditure ($‘000s) 3 5 7 6 3.5 4 4.5 7 7.5 8.5 Sales ($’000s) 50 250 700 450 75 150 200 750 800 1100 a. Estimate the slope and intercept coefficients of the linear regression model. (5 marks) b. If advertising expenditure is equal to $9,000, estimate the total Sales Income. (2 marks) Question 2 (7 marks) (Note this question is from the Week 6 Tutorial) Approximately three (3) out of every four (4) Australians who filed a tax return received a refund in a particular year. If three (3) individuals are chosen at random from among those who filed a tax return that year, find the probabilities of the following events; a. All three (3) received a refund. (3 marks) b. None of the three (3) received a refund. (2 marks) c. Exactly one received a refund. (2 marks) Question 3 (7 marks) (Note this question is from the Week 7 Tutorial) The number of accidents that occur on an assembly line have a Poisson distribution with an average of three (3) accidents per week. a) Find the probability that a particular week will be accident free. (3 marks) b) Find the probability that at least three (3) accidents will occur in a week. (2 marks) c) Find the probability that exactly five (5) accidents will occur in a week. (2 marks) 3 Question 4 (7 marks) (Note this question is from the Week 8 Tutorial) MNM Corporation gives each of its’ employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken from population of 500. a. What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14? (3 marks) b. What is the probability that the average aptitude test in the sample will be greater than 82.68? (2 marks) c. What is the probability that the average aptitude test in the sample will be less than 78.69? (2 marks) Question 5 (11 marks) (Note this question is from the Week 10 Tutorial) A random sample of 25 was drawn from a normal distribution whose standard deviation is 5. The sample mean was 80. a) Determine the 95% confidence interval estimate of the population mean. (3 marks) b) Repeat the part (a) with a sample size of 100. (3 marks) c) Repeat the part (a) with a sample size of 400. (3 marks) d) Describe what happens to the confidence interval estimate when the sample size increases. (2 marks) Question 6 (11 marks) (Note this question is from the Week 11 Tutorial) A random sample of ten (10) observations was drawn from a large population, as shown below. 7 12 8 4 9 3 4 9 5 2 Test to determine if we can infer at the 5% significance level that the population mean is not equal to five (5) using the following steps (a. – f.) listed below: a. State the hypotheses. (1 mark) b. State the relevant test statistic and the reason for the selection. (1 mark) c. State the Level of significance. (1 mark) d. State the Decision rule. (4 marks) e. Calculate the test statistics. (2 marks) f. State the conclusion based on the above steps. (