(a)  Explain what is meant by a ‘significance test’ and give an example of how significance testing could be used in business decision-making.

(b)  In a simple random sample of 500 households in Glasgow, 25 per cent stated that they would be interested in participating in a car-sharing scheme. In a similar survey of 400 households in Manchester, 30 per cent expressed an interest in participating in such a scheme. To test whether the difference between the two sample results is statistically significant, you are required to:

(i) State the appropriate null and alternative hypotheses for your test.

(ii) Find the critical value of z for a two-tailed test at the 5% level.

(iii) Calculate the test statistic and interpret the result.

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