In order to investigate the average amount spent on liability insurance by firms in the clothing industry, a random sample of 64 firms is selected. The sample mean is found to be £17,500 per annum with a sample standard deviation equal to £2,500.

(a) Calculate 95% and 99% confidence intervals for the population mean.

(b) Calculate the sample size required to estimate annual mean spending by clothing firms on liability insurance to within £450 with 95% confidence.

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