Find the minimum sample size n needed to estimate u for the given values of c, s, & E. c=0.98, s=6.5, & E=1.?
I did a problem up the page from here and you would do it the same way.
To find the minimum sample size needed to estimate u (the population mean) with a desired level of confidence, we can use the formula:
n = (Z^2 * s^2) / E^2
Where:
- n is the sample size
- Z is the Z-value, which corresponds to the desired level of confidence
- s is the standard deviation of the population
- E is the desired margin of error
In the given question, we have:
- c = 0.98 (desired confidence level)
- s = 6.5 (standard deviation)
- E = 1 (desired margin of error)
Step 1: Find the Z-value for the desired confidence level.
Since c = 0.98 represents a 98% confidence level, we need to find the corresponding Z-value. The Z-value is obtained from the standard normal table or using a statistical calculator. For a 98% confidence level, the corresponding Z-value is approximately 2.33.
Step 2: Substitute the values into the formula to calculate the sample size (n):
n = (Z^2 * s^2) / E^2
= (2.33^2 * 6.5^2) / 1^2
= (5.4289 * 42.25) / 1
≈ 229.135
Therefore, the minimum sample size (rounded up to the nearest whole number) needed to estimate u with a 98% confidence level, a standard deviation of 6.5, and a margin of error of 1 is 230.