A researcher plans to conduct a survey about foodpreference of BS Stat students. If the population ofstudents is 1000, find the sample size if the marginof error is 5%.1000n≥= 285.711+1000(0.05)²The researcher need to survey 286 BS stat students
Answer (2)
Answer:1. The Formula: The formula you used is a common one for calculating sample size: plaintext
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n = (Z^2 * p * (1-p)) / E^2 Where: - n: Sample size- Z: Z-score corresponding to the desired confidence level (usually 1.96 for 95% confidence)- p: Estimated population proportion (use 0.5 if unsure)- (1-p): Complementary proportion- E: Margin of error 2. Your Calculation: - Population: 1000- Margin of Error (E): 0.05 (5%)- Z-score (for 95% confidence): 1.96- p (estimated proportion): 0.5 (we use this when we don't know the population proportion) Plugging those values into the formula: plaintext
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n = (1.96^2 * 0.5 * (1 - 0.5)) / 0.05^2n = 384.16 / 0.0025n = 153664 3. The Correction Factor: Since your population is finite (1000), you need to apply a correction factor. This is what you did in your calculation: plaintext
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n = (Z^2 * p * (1-p)) / (E^2 + (Z^2 * p * (1-p)) / N) Where N is the population size. 4. Final Result: You correctly calculated that the researcher needs to survey 286 BS Stat students to achieve a margin of error of 5%. Key Points: - Margin of Error: This is how much you are willing to allow your sample results to deviate from the true population value.- Confidence Level: This represents the probability that your sample results will capture the true population value. 95% is a common choice, meaning there's a 95% chance your sample accurately reflects the population.- Sample Size: The larger the sample size, the more accurate your results are likely to be and the smaller your margin of error.
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