The credit data file CREDIT12.XLS represents a random sample of 118 data records for individuals applying for credit at a well-known store. The file is available on the Excel sheet and the meaning of the field variables is given overleaf.

Attempt the following tasks, showing your working when appropriate:

1 Based on this sample, and clearly showing workings, appropriate graphics and your response to blank values in the data, calculate the following:
(a) the probability of randomly picking two men under 40 from the sample
(b) given that we’re picking from men in the sample, the probability of picking a
man whose job income is between £2,000 and £3,000 per month
(c) a sub-sample group of five unmarried men under 35 are to share their more detailed views of credit in a focus group. Calculate how many different ways are there of putting these groups of five together from this sample?

2 Assume that Total Income is the sum of Job Income and Additional Income.
(a) produce frequency distributions, histograms and appropriate descriptive statistics which allow a comparison of Total Income for men, with Total Income women
(b) provide some interpretive comment on the statistical and graphical output produced, focusing both on similarities and differences between the two groups observed
(c) comment on the effect that outlying data values have on the results obtained, and your consequent response to the presence of outliers in this case

3 Assuming that the descriptive statistics for the distribution of Ages in this sample are good estimates of the parameters that apply to the background population, and that this background population is near-normally distributed, calculate the following using the z-table and/or Excel functions, clearly showing your workings :
(a) the % of the population of applicants under 45
(b) the % of the population of applicants between 25 and 35
(c) the lower age limit for the oldest 25% of the population of applicants
(d) how do the two answers in (a) and (b) above compare with the actual % proportions for this sample, provide explanatory comment on the differences

4 Construct 95% confidence intervals for the mean Job Income of the background population of both men granted credit, and separately for women not granted credit, (the z-table and/or t-table and/or Excel functions can be used) clearly showing your workings:
(a) Clearly state the two intervals, explaining the meaning of the figures
(b) Provide interpretation, focusing again on differences between the two groups, paying attention to whether the two confidence intervals overlap or not
(c) Comment on the sample sizes here and their consequent implication

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