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A study was conducted to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours.We are 95% confident that the mean number of weekly hours that U.S. adults use computers at home falls between which of the following intervals?Group of answer choices7.7 and 9.37.3 and 9.76.5 and 10.58.4 and 8.68.1 and 8.9

Question

A study was conducted to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours.We are 95% confident that the mean number of weekly hours that U.S. adults use computers at home falls between which of the following intervals?Group of answer choices7.7 and 9.37.3 and 9.76.5 and 10.58.4 and 8.68.1 and 8.9

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Solution

To find the confidence interval, we use the formula for a confidence interval for a population mean:

CI = x̄ ± Z * (σ/√n)

where: x̄ is the sample mean, Z is the Z-score (for a 95% confidence interval, Z = 1.96), σ is the population standard deviation, and n is the sample size.

Given in the problem, we have x̄ = 8.5 hours, σ = 3.6 hours, and n = 81.

Substituting these values into the formula, we get:

CI = 8.5 ± 1.96 * (3.6/√81) CI = 8.5 ± 1.96 * (3.6/9) CI = 8.5 ± 1.96 * 0.4 CI = 8.5 ± 0.784

So, the 95% confidence interval is (8.5 - 0.784, 8.5 + 0.784) = (7.716, 9.284).

Therefore, the mean number of weekly hours that U.S. adults use computers at home falls between 7.7 and 9.3 hours with 95% confidence.

This problem has been solved

Similar Questions

A study was conducted to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours.A similar study conducted a year earlier estimated that μ, the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year.Using a 95% confidence interval of (7.7, 9.3), which of the following is an appropriate conclusion? The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. You cannot draw a conclusion because the only way to reach a conclusion is to find the p-value of the test.

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