The do-it-yourself (DIY) consumer movement has had a profound impact on the retailing business. A recent study conducted by the Centre for Consumer Research examined various traits of persons classified as 'do-it-yourselfers' and 'non-do-it- yourselfers'. One factor considered was a person's age. Because younger people are generally healthier but less affluent, it is reasonable to expect do-it-yourselfers to be younger. The ages (in years) of the people in the two groups from the study are summarised as follows:
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DIY consumers
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Non-DIY consumers
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Sample mean (years)
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41.8
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47.4
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Standard deviation
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15.9
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16.2
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Sample size
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29
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34
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Does the data support the hypothesis that do-it-yourselfers are younger, on average, than non-do-it-yourselfers?
(a) Define the two populations and then formulate the appropriate null and alternative hypothesis for the test.
(b) Conduct a hypothesis test at the 10% level of significance to test the null hypothesis.
(c) What statistical and management conclusion can be drawn from the findings?
(d) Will the conclusion differ if the hypothesis test was conducted at the 5% level of significance? Justify your answer statistically.