Question

In a study to understand the average number of weekly grocery shopping trips during the May 2020 stay-at-home order in Michigan, with a 95% confidence level and a margin of error of 1 trip or less, what is the necessary sample size?

a) 153
b) 213
c) 289
d) 324

Answer 1

To determine the necessary sample size, we need to use the formula: Sample Size = (Z-score)^2 * (Standard Deviation^2) / (Margin of Error^2). Since the margin of error is given as 1 trip or less, we can assume it to be 1. The Z-score for a 95% confidence level is approximately 1.96. The standard deviation is unknown in this case, so we need to estimate it based on previous data or pilot studies.

Step-by-step explanation:

To determine the necessary sample size, we need to use the formula:

Sample Size = (Z-score)^2 * (Standard Deviation^2) / (Margin of Error^2)

Since the margin of error is given as 1 trip or less, we can assume it to be 1. The Z-score for a 95% confidence level is approximately 1.96. The standard deviation is unknown in this case, so we need to estimate it based on previous data or pilot studies. Once we have the estimated standard deviation, we can substitute these values into the formula to calculate the necessary sample size.

Using the formula, the necessary sample size is:

Sample Size = (1.96)^2 * (Standard Deviation^2) / (1^2)

Without the value for the standard deviation, we cannot calculate the exact sample size. Therefore, none of the provided options (a) 153, (b) 213, (c) 289, or (d) 324 can be considered as the necessary sample size.