A researcher is conducting a study to estimate the average monthly household expenditure on groceries in a city. The researcher wants to ensure a 97% confidence level. The population size of households in the city is estimated to be 5000. Using Slovin's formula, calculate the required sample size for this study.
Question
A researcher is conducting a study to estimate the average monthly household expenditure on groceries in a city. The researcher wants to ensure a 97% confidence level. The population size of households in the city is estimated to be 5000. Using Slovin's formula, calculate the required sample size for this study.
Solution
To calculate the required sample size using Slovin's formula, we first need to understand the formula itself. Slovin's formula is given by:
n = N / (1 + Ne^2)
where:
- n is the sample size
- N is the total population size
- e is the margin of error
The margin of error (e) can be calculated from the confidence level. A 97% confidence level corresponds to a 3% margin of error (100% - 97% = 3%). Therefore, e = 0.03.
Now, we can substitute N = 5000 and e = 0.03 into Slovin's formula:
n = 5000 / (1 + 5000*(0.03)^2)
Solving this equation will give us the required sample size.
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