C. Determine the sample size, given the following data: (s – sample standard deviation)
1. s= 7, E = 3.65, confidence level: 98%
2. s=4, E = 2.76, confidence level: 99%
1. s= 7, E = 3.65, confidence level: 98%
2. s=4, E = 2.76, confidence level: 99%
Answers & Comments
Answer:
24
Step-by-step explanation:
The formula to calculate the sample size is:
n = (Z^2 * s^2) / E^2
where n is the sample size, Z is the Z-score corresponding to the desired confidence level, s is the sample standard deviation, and E is the desired margin of error.
For a 98% confidence level, the Z-score is 2.33, and for a 99% confidence level, the Z-score is 2.58.
Using these values and the given s and E, we can calculate the sample size for each scenario:
1. n = (2.33^2 * 7^2) / 3.65^2 = 47.26 ≈ 48 (rounded up to the nearest whole number)
So, the sample size is 48.
2. n = (2.58^2 * 4^2) / 2.76^2 = 23.41 ≈ 24 (rounded up to the nearest whole number)
So, the sample size is 24.