LUBS5012 Research Methods
Answer the questions initially using statistical tables. Then repeat using Excel.
1. Hypothesis Testing, Population Mean
In the week before Christmas it was hoped that the mean takings of a shop’s branches would
be £40,000. However, 40 randomly sampled branches have mean takings of only £37,000
with a standard deviation of £6,000. Does this suggest that the mean takings of all the
branches was significantly different from the target figure? (1% level of significance)
2. Hypothesis Testing, Population Proportion
A bank claims that 60% of people who apply for a personal loan will be granted it. However,
a random sample of 500 loan applicants contains only 250 which are successful. Does this
suggest that the success rate is significantly different from 60%? (5% level of significance)
3. Hypothesis Testing, Goodness of Fit
A telephone sales company with 200 sales staff uses a five-level grading system for annual
performance. End-of-year bonus payments for sales staff are determined on their individual
performance grading. Staff rated Grade 1 receive only the minimum bonus payment while
staff rated Grade 5 receive the highest bonus payment. The company has an expected
distribution of performance grades which it uses to budget for bonus payments. However the
company’s financial director is concerned that the actual distribution of performance grades
differs significantly from the expected distribution with proportionally fewer sales staff
getting the lower grades and proportionally more getting higher than expected grades. Based
on the latest performance grades, is the financial director right to be concerned? Use a 5%
significance level.
4. Additional Question
A packaging device is set to fill detergent packets with a mean weight of 500g. It is important
to check the machine periodically because overfilling increases the cost of materials whereas
underfilling leaves the firm liable to prosecution. A random sample of 25 filled packets is
weighed and shows a mean net weight of 510g with a standard deviation of 15g. What
conclusion can be drawn at the 5% level of significance?
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