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Refer to the data provided in the Q1 Best T-shirts Excel spreadsheet based on your group number.
Best T-shirts Ltd sells adult t-shirts in seven sizes. The table below shows the length and width of each t-shirt size.
Adult T-shirt sizes T-shirt size Length in inches Width in inches Small 27 18 Medium 28 19 Large 29 22 XL 30 23 XXL/2XL 31 25 XXXL/3XL 34 27 XXXXL/4XL 35 28
A summary of the sales in the month of March 2016 is provided in the Q1 BestT-shirts spreadsheet. The store manager uses the numbers 1 to 7 to record sales of the different t-shirts in a particular month. You are provided with the following key for interpreting the data:
1=Small, 2=Medium, 3=Large, 4=XL, 5=2XL, 6=3XL, 7=4XL
Required: Use the data allocated to your group to answer question a) to g).
a) Copy and paste the data for your group to a new spreadsheet. (1 marks) b) Use the Excel COUNTIF function to prepare a frequency distribution for the sales of Best T-shirts Ltd. (4 marks) c) Use the Excel COUNT function to calculate the number of T-shirts sold in March 2016. (1 mark) d) Calculate the relative frequencies and cumulative frequencies for the frequency distribution you constructed in part (a) of this question. Show all your workings. (4 marks) e) Which measure of central tendency best represents this data? Give reasons for your answer. (2 marks) f) Use a suitable graph to summarize the sales based on the T-shirt sizes. Ensure that the graph is titled and labelled. (3 marks) g) Which t-shirt size is in high demand? Which t-shirt size is in low demand? (2 marks) h) Management is considering discontinuing the production of the 2XL, 3XL and 4XL tshirts. Use last month’s data to approximate the proportion of the customers who would be affected by this decision. (2 marks) i) Identify the level of data measurement for the three variables: T-shirt size, Length in inches and width in inches. Give reasons for your answer (6 marks)
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Question 2 (12 marks)
Refer to the data provided in the Q2 KidsandTV Excel spreadsheet based on your group number.
The sponsors of television shows targeted at children wanted to know the amount of time children spend watching television, since the types and number of programs and commercials presented are greatly influenced by this information. As a result, a survey was conducted to estimate the average number of hours Australian children spend watching television per week. From past experience, it is known that the population standard deviation is 6.5 hours. Assume the hours spent watching television is normally distributed. The data in table 4-1 was gathered from a sample of 100 children.
Required:
a) Use the Excel AVERAGE function to find the sample mean number of hours spent watching television per week. (1 mark) b) Use the Excel STDEV.S function to find the sample standard deviation of the number of hours spent watching television per week. (1 mark) c) Should you use the standard normal distribution, the t-distribution or neither to construct a 96% confidence interval for the population mean number of hours spent watching television per week? Explain your reasoning. (2 marks) d) What is the point estimate of the population mean? (1 mark) e) Find the margin of error for the 96% confidence interval. Show all your workings (3 marks) f) Construct a 96% confidence interval for the population mean. Interpret the results. (4 marks)
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Question 3 (13 marks)
St Francis Smith Hospital has provided some information on nine kinds of surgeries in the first week of March 2016. The following table shows the number of patients and the probability of success of each kind of surgery.
Type of Surgery Number of Patients
Probability of success Knee and Hip Replacement Surgery 8 0.8 Strabismus (Lazy eye) Surgery 9 0.5 Coronary Artery Bypass Graft (Heart) Surgery 7 0.78 Hernia Surgery 6 0.85 Microdiscectomy spine surgery 5 0.90 Endoscopic Plantar Fasciotomy surgery 7 0.83 Heart transplant surgery 6 0.85 Kidney transplant surgery 7 0.90 Liver transplant surgery 5 0.78 Lumbar Laminectomy surgery 5 0.65
Answer this question based on the type of surgery allocated to your group. For example, group 3 should answer the questions that follow based on information provided for the Coronary Artery Bypass Graft surgery.
Required: a) Use Excel’s BINOMDIST function to prepare a binomial probability distribution for the number of patients whose surgery was a successful. (Helpful hint: To calculate the binomial probabilities you need to use Excel’s probability mass function. So type FALSE in the cumulative (i.e. the last) part of the formula). (4 marks) b) Calculate the mean, variance and the standard deviation of the binomial distribution you prepared in part (a) of this question. (6 marks) c) Interpret the results calculated in part (b) of this question (2 marks) d) What values of x would you consider unusual (1 mark)
Group Number Type of Surgery 1 Knee and Hip Replacement Surgery 2 Strabismus (Lazy eye) Surgery 3 Coronary Artery Bypass Graft (Heart) Surgery 4 Hernia Surgery 5 Microdiscectomy spine surgery 6 Endoscopic Plantar Fasciotomy surgery 7 Heart transplant surgery 8 Kidney transplant surgery 9 Liver transplant surgery 10 Lumbar Laminectomy surgery
