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A researcher wants to conduct a study to determine the satisfaction level of customers at a local restaurant. The researcher wants to ensure a margin of error of 5% at a 95% confidence level. The population size of customers who frequent the restaurant is estimated to be 1000. Using Slovin's formula, calculate the required sample size for this study. 10 pointsYour answer

Question

A researcher wants to conduct a study to determine the satisfaction level of customers at a local restaurant. The researcher wants to ensure a margin of error of 5% at a 95% confidence level. The population size of customers who frequent the restaurant is estimated to be 1000. Using Slovin's formula, calculate the required sample size for this study. 10 pointsYour answer

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Solution

To calculate the required sample size using Slovin's formula, follow these steps:

  1. Identify the desired margin of error (e) and the population size (N). In this case, e = 0.05 (5%) and N = 1000.

  2. Slovin's formula is given by N / (1 + Ne^2). Substitute the values of N and e into the formula.

  3. The calculation will be as follows: 1000 / (1 + 1000*(0.05)^2).

  4. Solve the equation: 1000 / (1 + 1000*0.0025) = 1000 / (1 + 2.5) = 1000 / 3.5 = 285.71.

  5. Round up to the nearest whole number because you can't have a fraction of a participant. So, the required sample size for this study is approximately 286.

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