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ETB1100 Business Statistics, S2 2014
Assignment 2 Topic: Inference & Simple linear regression
Due date: 11 am, Thursday of Week 11 (16th October 2014)
• ASSIGNMENTS WITHOUT SIGNED COVER SHEETS WILL NOT BE ACCEPTED
• This assignment is to be submitted in a print form.
• A penalty of 10% per day will apply to late assignments, unless extension on assignment due date has been sought with valid documentary evidence.
• Post your completed assignment in assignment box labelled ‘ETB1100 Bus Statistics’ and located on the first floor of Berwick campus building 901 near Faculty of Bus & Eco Student Services. (You must be able to provide a replacement copy of the assignment if this is requested. Make sure you keep a printed copy and an electronic copy as back-up.)
Assignment Weight: 15% Note: This assignment will be marked out 75 marks.
Data for Assignment 2: See file ETB1100_A2_Data.xls in Assignment 2 Section on the unit’s website in Moodle.
Note: In answering parts of the questions where statistical inference is conducted, you must include some or all of the following (as appropriate) for full credit:
1. the reason for using a particular formula or distribution 2. the null and alternative hypotheses 3. the critical value(s) used 4. the level of significance 5. the distribution of the statistic employed in a test, and 6. the conclusion.
• Answers to Question 3 of this assignment must be supported by Regression Summary Output
generated using Excel.
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Question 1 (7+2+2+6+4+4 = 25 marks)
The manager of a local fast-food restaurant is interested in improving the services provided to customers who use the restaurant’s drive-up windows. As a first step in this process, the manager asks his assistant to record the time (in minutes) it takes to serve a large number of customers at the final window in the facility’s drive up system. For a random sample of 50 customers selected during the busiest hours of the day, the service times are given in worksheet Qn1 of file ETB1100_A2_Data.xls.
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(a) Using this sample of service times, obtain a 90% confidence interval estimate for the mean service time of all customers arriving during the busiest hours of the day at this fast-food operation.
(b) Interpret the confidence interval constructed in part (a).
(c) What assumption did you make in obtaining the confidence interval in part (a)?
(d) Now using your random sample of 10 customers and their service times from Assignment 1 Question 2 obtain a 90% confidence interval estimate for the mean service time of all customers arriving during the busiest hours of the day at this fast-food operation.
(e) Compare the widths of the confidence intervals obtained in parts (a) and (d), commenting and giving a possible reason for the discrepancy.
(f) Explain which confidence interval, part (a) or (d), is likely to produce more stable (reliable) estimate for the mean service times of all customers arriving during the busiest hours of the day at this fast-food operation and why.
Question 2 (7+4+4 = 15 marks)
A quality control manager at a factory that manufactures memory cards for digital cameras wishes to determine whether the mean data transfer rate of a large shipment of cards is equal to 10MB/s (that is, 10 Megabytes per second).
The quality control manager finds the data transfer rates for a random sample of 64 memory cards, which are given in worksheet Qn 2 of file ETB1100_A2_Data.xls.
(a) On the basis of the given sample, can the manager conclude at the 5% level of significance that there is no evidence of the mean data transfer rate to be different from 10 MB/s? Perform the hypothesis test using the critical value approach.
(b) What is the p-value for the test you performed in (a)? Interpret this value.
(c) Would your conclusion change if it was known that the population standard deviation of the transfer rates is 0.8? Show all details to support your answer.
Question 3 (4+2+6+4+4+6+6+3 = 35 marks)
The owner of the Pizza Delight restaurant chain would like to understand the relationship between the quantities sold (Y) and the price of its speciality thick-crust pizza (X). The owner has gathered data on the number of pizzas sold last month and the pizza price for his 20 outlets in Melbourne, Australia. These data are provided in worksheet Qn3 of file ETB1100_A2_Data.xls.
(a) Obtain scatter plot of Y against X and describe the type of relationship between these variables.
The owner of the Pizza Delight restaurant chain has proposed the fitting of a linear regression model between the number of pizzas sold and the price.
(b) On the basis of analysis in part (a), explain why do you think that it is reasonable to fit the model proposed by the owner?
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(c) Provide the theoretical linear regression model linking variables ‘Quantity sold’ and ‘Price’ which can be used by the owner. Use Excel to fit this model and report the estimated equation. Has the sign of the estimate for β1 turned out as indicated by the scatter plot?
(d) Interpret the estimated coefficients for β0 and β1.
(e) Report the value of coefficient of determination. Explain, what information about the usefulness of this fitted model is conveyed by this value? Is this a useful model?
(f) At 5% level of significance, can we say that there is a significant negative linear relationship between the quantity sold and the price of pizza? Show all details to support your answer.
(g) Showing all relevant details obtain a 90% confidence interval for the slope β1? On the basis of this interval, can we say that there is a significant negative linear relationship between the quantity sold and the price of pizza? Explain.
(h) Predict quantity sold if the owner sets the price of thick-crust pizza at $20. Is this predicted value a reliable estimate? Explain.
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