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# I need the answer to the questions: 1. A consultant for Dell

### Customer Question

HI I need the answer to the questions:
Customer: 1. A consultant for Dell was investigating computer usage among students at a particular university. 200 undergraduates and 100 postgraduates were chosen and asked if they owned a laptop. It was found that 81 of the undergraduates and 63 of the postgraduates owned a laptop. The consultant calculated that 48% (144 out of 300) of the students interviewed owned a laptop. Explain, with reasons, whether the figure of 48% would be a good estimate of the proportion of all students who own a laptop.
Hint: The answer is ‘Well James, it depends!’, but obviously reasons are required!
(10 marks)
2. A 95% confidence interval for the mean income of shop assistants in a certain city, based on a random sample of n shop assistants, is found to be (£18,000, £21,000). Explain what this means briefly (in at most 2–3 sentences). Would a 90% confidence interval be better than a 95% confidence interval? Justify your answer.
Hint: The answer is ‘Well James, it depends!’, but obviously reasons are required!
(10 marks)
3. For a certain variable, the standard deviation in a large population is equal to 16. How large a random sample is needed to be 99% confident that the sample mean is within 2 units of the population mean? Would you recommend a confidence level other than 99%?
Hint 1: Use the confidence interval Excel utility.
Hint 2: The answer is ‘Well James, it depends!’, but obviously reasons are required!
(10 marks)
4. An accounting firm wishes to test the claim that no more than 6% of a large number of transactions contain errors. In order to test this claim, they examine a random sample of 225 transactions and find that exactly 20 of these are in error. What conclusion should the firm draw? Use a 5% significance level.
Hint: Use the hypothesis testing Excel utility (one population).
5. Explain (in no more than a paragraph for each) the purpose of:
(a) sampling
(b) hypothesis testing.
Discuss any advantages and limitations of each.
2
(10 marks)
(10 marks)
6. A lumber company makes plywood for the furniture industry. One product it makes is 3/4-inch panels. It is very important that the panels conform to specifications. One specification calls for the panels to be made to an average thickness of 0.75 inches. Each hour, 5 panels are selected at random and measured. After 20 hours, a total of 100 panels have been measured (so the sample size is n = 100). The data are in the file ‘Lumber.xls’.
(a) Based on the sample data, what should the company conclude about the status of its product meeting the thickness specification? Test at a 1% significance level. Discuss your results in a brief ‘executive summary’ to the production manager.
Hint: Use the hypothesis testing Excel utility (one population).
(b) The production manager has looked at the results of your test. He wishes to repeat this sampling process and wants a rule to compare future X ̄ values only. So, based just on a sample mean of any new random sample of panels, without having to conduct a formal hypothesis test, he wishes to decide whether the thickness specification is being met, again using a 1% significance level. Develop a suitable rule.
Hint: Use the hypothesis testing Excel utility (one population).
(c) The manager wishes to know what type of error in (a) could have been made and what the potential consequences of the error might be.
(25 marks)
7. A bookstore samples its order record to examine the number of days between placing an order and receiving the goods. The results (in days) are shown below.
Assess and comment on the differences between surface transportation and air freight. You may use Excel! The data are in the file ‘Bookstore.xls’.
Hint: This question is deliberately open-ended. You may investigate the data any way you like, for example calculating some descriptive statistics.
Surface transportation
18
20
24
23
28
32
24
39
18
29
25
27
19
24
21
19
24
27
33
37
15
20
26
21
17
26
25
23
25
35
Air freight
12
12
13
21
18
14
9
16
18
14
13
11
15
11
17
14
12
13
11
17
19
16
14
14
12
JA: Is there anything else the tutor should be aware of?
Customer: no
Submitted: 4 months ago.