Question

What sample size is needed to give the desired margin of error within ±2.5 with 95% confidence, assuming the previous sample had =30 ?

Select answer from the options below

1) 139

2) 390

3) 554

4) 658

Answer 1

To calculate the required sample size for a desired margin of error of ±2.5 with 95% confidence, you can use the formula (Za/2 * standard deviation / desired margin of error)^2. Using the previous sample size of 30, the required sample size is 658.

Step-by-step explanation:

To calculate the required sample size for a desired margin of error within ±2.5 with 95% confidence, we can use the formula:

sample_size = (Za/2 * standard_deviation / desired_margin_of_error)2

Using the previous sample size of 30, we can calculate the standard deviation as follows:

standard_deviation = (previous_sample_size / Za/2) * desired_margin_of_error

Substituting the values into the formula, we get:

sample_size = (1.645 * 30 / 2.5)2 = 658

Therefore, the sample size needed is 658.