1. Use Excel to obtain a random sample of 30 members of staff in this file. Ensure that there are no duplicates in this sample. Print out the full details of these records, including the titles at the head of each column
2. For the variable Salnow, calculate 95% and 99% confidence intervals for your sample mean. Show all your workings.
3. In the case of the confidence intervals calculated in (2), what is the precision of the estimates? What size sample would you need in order to halve the precision? All calculations must be shown.
4. Obtain the mean and standard deviation, for the whole population of the company, for the variable Salnow. What would be the probability of obtaining a sample of size 30 people whose mean current salary was above £12,000? For this question, assume that the distribution of the Salnow variable is normal.
5. This question must be completed by hand showing full calculations.
A firm is about to market a new proprietary cold remedy, and desperately needs information concerning expenditure on pharmaceuticals. In particular, they would like to know how much each person spends on cold remedies. A major postal survey is to be undertaken. However, the firm has already carried out a small pilot survey involving 35 members of the public, and has the following summary data:
X = 3865 X2 = 438,119
where X = the amount spent on cold cures per person per year.
(a) Using the above pilot sample data, calculate a 95% confidence interval for the average amount spent on cold remedies per person per year.
(b) In deciding the specifications for the full survey, the firm wish to estimate mean expenditure with a margin of error of ±£2.00, at the 95% confidence level. How large should the full sample be, in order to achieve this?
(c) The full survey will cost £500 in fixed costs. There is also a variable cost, per questionnaire, of £1.00 for each mailing, and a further