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.10 pointsYour answer
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.10 pointsYour answer
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 / (1 + Ne^2)
where: N = population size e = 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%). However, this needs to be expressed as a decimal in the formula, so we divide by 100 to get 0.03.
Now we can substitute the given values into the formula:
N = 5000 (the population size) e = 0.03 (the margin of error)
So the formula becomes:
5000 / (1 + 5000*(0.03)^2)
Now, calculate the expression in the parentheses:
1 + 5000*(0.03)^2 = 1 + 5000*0.0009 = 1 + 4.5 = 5.5
Then divide the population size by this result:
5000 / 5.5 = approximately 909.09
Since we can't have a fraction of a household, we round this up to the nearest whole number. So the required sample size for this study is 910 households.
Similar Questions
A marketing manager wants to conduct a survey to estimate the proportion of customers who are likely to repurchase a product. The manager wants a 90% confidence level. The population size of customers who have purchased the product in the past is estimated to be 2000. Using Slovin's formula, determine the required sample size for this survey.10 pointsYour answer
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
A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and an margin of error of $76 is desired, how many customers should be sampled?
Which of the following statements is true regarding sample size calculations?*1 pointA. Slovin's formula is used for determining the sample size for stratified sampling.B. Cochran's formula accounts for the margin of error and confidence level.C. Population size is not a consideration when calculating sample size.D. Slovin's formula is suitable for use in all types of sampling methods.
A group of marketing students at a large university wants to determine the proportion of first year students who use certain types of social media. The students want their estimate to be within 0.03 of the true proportion with a 95% level of confidence. Two years ago, a similar study determined the proportion to be 0.796. How large of a sample is required?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.