how large a sample size is needed for 2 sided 95% confidence interval to have a length of 2 weeks when mean is 3.6
To determine the sample size needed for a 2-sided 95% confidence interval with a length of 2 weeks, we need some additional information. Specifically, we need to know the population standard deviation or the estimated standard deviation (sample standard deviation) of the data.
Assuming that we don't have any information about the standard deviation, we can use a conservative estimate and assume that the population standard deviation is 1. This is commonly done when the population standard deviation is unknown.
To calculate the sample size, we can use the following formula:
n = (z * σ / E)²
Where:
- n represents the sample size,
- z represents the z-score corresponding to the desired confidence level (in this case, 95%),
- σ represents the standard deviation, and
- E represents the desired margin of error (half of the length of the confidence interval).
Plugging in the values we have:
- z = 1.96 (for a 95% confidence level)
- σ = 1
- E = 2/2 = 1
n = (1.96 * 1 / 1)²
n = 1.96²
n ≈ 3.8416
Since we can't have a fraction of a sample, we need to round up the value. Therefore, a sample size of at least 4 should be sufficient to achieve a 2-sided 95% confidence interval with a length of 2 weeks, assuming a population standard deviation of 1.