(d) A random sample of 100 customers in a supermarket showed that the average age was 35.4 years. In the past and traditionally the average age of customers had been 34 years. It is known that the standard deviation of customers’ ages is 8 years.
i.e. = 35.4 Standard Deviation = 8 n = 100
(i) Write out the hypothesis appropriate to test whether the average age of customers has changed.
(ii) Carry out the hypothesis test described in question 3d(i) above using a 95% level of certainty (α = 0.05). State your conclusion.
(iii) Suppose it was believed that an influx of older people to a new retirement home in the area had affected the customer profile of the supermarket. State the null and alternative hypothesis necessary to carry out the revised test.
(iv) Carry out the test described in part 3d(iii) above using a 95% level of certainty (α = 0.05). State your conclusion.
(e) Your conclusions to parts d(ii) and d(iv) may differ, despite being based on the same set of sample data. Explain carefully (with the aid of a diagram) why this is so.
(f) What is the probability of committing a Type 1 Error in your conclusions to parts d(ii) and d(iv)? What is a Type 1 Error?
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