Posted: September 1st, 2015

The null and alternative hypotheses

Data Analysis in Business
Assignment Topics: Data Collection & Sampling Designs, Statistical Inference on means and proportions forone and two populations Instructions:
•Remember the unit is “Data Analysis in Business”; some assignment tasks may not beprescriptive.
•All numerical answers must be generated using Excel. All Excel functions required for theassignments have been covered via tutorials & lecture material. Some Excel help is available viathe “Unit Guide & Resources” section in Moodle. For full credit, all relevant Excel outputs (notthe data provided) must be labelled clearly and made part of the answers to support yourexplanations. You may annotate these outputs for clarity. Please make sure that the Exceloutput appears on a single page and not divided between the pages.
•The data for this assignment is provided in file “DAiB Ass1-S2-2015data.xlsx”, and is placed in
Note: In answering parts of the questions where statistical inference is required, you must include some or allof the following for full credit:
1. the reason for using a particular formula or distribution
2. the null and alternative hypotheses
3. the critical value(s) or the p-value used ; the level of significance or the confidence level used
4. the distribution of the statistic employed in a test, and finally the conclusion.
Question 1(4+5+1+2+3+2+3 = 20 marks)
An offshore gas exploration company uses a large number of low cost components. The daily usageof the components is believed to be fairly constant. Each month the company orders a large numberof boxes containing 100 components each on a regular basis to keep up with the usage ofcomponents. The workers are required to enter in a computer system the number of componentsthat are taken out of a specific box for using; the boxes are numbered chronologically so that olderdeliveries/ arrivals are used first. The company management is surprised by the number of boxes ofcomponents that had to be ordered during the month of July. On a casual inspection of records, thecompany manager finds a number of mismatches between the entered number of components andthe usage reflected by the number of empty boxes. The management suspects that either workersforget to record the number of components taken out of a box or are stealing components from theboxes for private sale. Worksheet Ass1-Q1 in file DAiB Ass1-S2-2015data.xlsx has component usagerecorded in the computer system against each of 500 boxes of components received for the monthof July.
(a) The manager is suggesting the use of a simple random sample of 50 boxes from the 500boxes used in July to view the situation. Given that the proportion of such mismatches in thepast has been only 3%, what is the probability that the manager will find the proportion ofmismatches in a sample of 50 to exceed 5%?
(b) Select a simple random sample of 50 boxes, and obtain a 90% confidence interval estimatefor the proportion of mismatches in the month of July.
(c) Based on the confidence interval estimate obtained in part (b), can we suggest to themanger that the proportion of mismatches is still 3%?
(d) Assuming that the proportion of mismatches is still 3%, is a sample of 50 boxes large enoughto provide the manager a 90% assurance that the margin of estimation error will not exceed2%?
(e) A new member on the management team suggested that a systematic random samplewould be better, because such a sample will be able to detect any cyclical pattern in theusage. Select a systematic random sample of 50 boxes.
(f) Report estimates of the standard error of the sample proportions of mismatches based onthe two samples obtained in parts (b) and (e). How do the two estimates compare?Comment.
(g) Assuming that the workers who forget to record the usage became slack and negligent asthe month progressed, which sampling method (systematic random or simple random) islikely to reflect this feature of the data better and why?
Question 2 (2+8+2+3+5 = 20 marks)
Choice-Mart offered 20% discount on all items purchased on Easter Monday. The manager of
Choice-Mart is interested in finding out whether purchasing behaviour (the amount spent in a singletransaction) of customers is related to their gender. He asked the checkout personnel to keep recordof the gender of the customer making the payment. At the conclusion of the sales on Easter Monday,he records the amount spent and the gender of the 150 randomly selected customers. These dataare given in worksheet Ass1-Q2 of data file DAiB Ass1-S2-2015data.xlsx.
(a) Describe the variable type and the measurement scale of variables Gender and AmountSpent.
(b) Can we conclude at 5% level of significance that on average females spend more money in asingle transaction than males? Provide all necessary details on the test(s) required tosupport your answer, giving reason (s) for the choice of your test.
(c) What assumptions did you make in performing test (s) in part (b)?
(d) Report the proportions of males and females who spent more than $120 during EasterMonday sales.
(e) On the basis of sample evidence, can we conclude that there is no difference in theproportions of males and females who spent more than $120?

Do you want your assignment written by the best essay experts? Order now, for an amazing discount.