According to Scarborough Research, more than 85% of working adults commute by car. Of all U. S. cities, Washington, D. C., and New York City have the longest commute times. A sample of 25 commuters in the Washington, D. C., area yielded the sample mean commute time of 27.97 minutes and sample standard deviation of 10.04 minutes. Construct and interpret a 99% confidence interval for the mean commute time of all commuters in Washington D. C. area.

The 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is (22.35, 33.59).

Step-by-step explanation:

The (1 - α) % confidence interval for population mean (μ) is:

Here the population standard deviation (σ) is not provided. So the confidence interval would be computed using the t-distribution.

The (1 - α) % confidence interval for population mean (μ) using the t-distribution is:

Given:

*Use the t-table for the critical value.

Compute the 99% confidence interval as follows:

Thus, the 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is (22.35, 33.59).

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