How large a sample of U.S. adults is needed in order to estimate U with a 95% confidence interval of length 1.2 hours?

I assume this was part of your previous post:

A study was conducted in order to estimate u, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults give a mean weekly computer usage time of 8.5 hours and that from prior studies , the population standard deviation is assumed to be 3.6 hours.

If so, use this formula:

Margin of error = z-value * sd/√n

With your data:

1.2 = 1.96 * 3.6/√n

Solve for n.

136

To determine the sample size needed to estimate a population parameter with a specific level of confidence, we need to consider several factors such as the desired confidence level, the estimated standard deviation or variance, and the acceptable margin of error.

In this case, you mentioned that you want a 95% confidence interval for the population mean (U) with a length of 1.2 hours. However, we'll need additional information to estimate the sample size accurately. Specifically, we need to know the estimated standard deviation or variance of the population (denoted as sigma or s).

Once we have this information, we can use the formula for sample size calculation:

n = ((Z * sigma) / E)²

Where:
n = Sample size needed
Z = Z-score corresponding to the desired confidence level (e.g., for a 95% confidence level, Z = 1.96)
sigma = Standard deviation of the population (if known); otherwise, use s, the sample standard deviation from a pilot study or previous data
E = Margin of error (half the desired interval length, in this case, 1.2/2 = 0.6)

Without the information about the population standard deviation or variance, we can't calculate an exact sample size. However, to provide an example, let's assume that the standard deviation is 10 hours (this is just a hypothetical value).

Using the formula:
n = ((1.96 * 10) / 0.6)²
n = (19.6 / 0.6)²
n ≈ 326.71

Therefore, for an estimated standard deviation of 10 hours and a desired confidence interval length of 1.2 hours, we would need a sample size of approximately 327 U.S. adults.

Remember, this calculation is based on the assumption of a hypothetical standard deviation, so it's crucial to have accurate information about the population's variability to obtain a more precise sample size.