Question: A researcher in Human Resources Management wants to determine the mean monthly salary of bank managers, and has a budget of $£ 1100$ to conduct a survey and construct a confidence interval based on survey responses. The researcher knows that the population standard deviation of monthly salary \(\sigma\) is $£ 1000$, and allows $£ 1.50$ to cover the cost of contacting each respondent. If the error in estimating the mean is to be less than $£ 100$ with a \(95 \%\) level of confidence, show that the required sample size is within budget.

- Is the budget sufficient if the researcher wishes to work with a \(99 \%\) level of confidence?

- What budget is required if the researcher wishes to retain a \(95 \%\) level of confidence, but wishes to reduce the associated error to $£ 50$ ?

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