A researcher wishes to estimate the mean response of a variable for a population of individuals, µ. It is believed that individuals in the population have values that vary by a population standard deviation of value 17.25. The researcher wishes to infer the value of the population mean by taking a random sample of individuals from the population and calculating a 99% confidence interval. In doing so he wishes to ensure that the margin of error is less than 5. What is the minimum size sample the researcher needs to take in order to achieve this?
A researcher wishes to estimate the mean response of a variable for a population of individuals, µ. It is believed that individuals in the population have values that vary by a population standard deviation of value 17.25. The researcher wishes to infer the value of the population mean by taking a random sample of individuals from the population and calculating a 99% confidence interval.
In doing so he wishes to ensure that the margin of error is less than 5.
What is the minimum size sample the researcher needs to take in order to achieve this?
We have given that,
Population standard deviation (σ) = 17.25 and Margin of error (E) ≤ 5 and confidence interval = 99%
Then,
Significance level (α)= 1- 0.99 = 0.01
Then,
We wil find the required minimum sample of size (n) = ?
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