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 h

Question

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.

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1 month 2021-10-26T17:18:31+00:00 1 Answer 0 views 0

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    2021-10-26T17:19:57+00:00

    Answer:

    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:

    CI=\bar x\pm z_{\alpha /2}\frac{\sigma}{\sqrt{n}}

    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:

    CI=\bar x\pm t_{\alpha /2,(n-1)}\frac{s}{\sqrt{n}}

    Given:

    \bar x=27.97\\s=10.04\\n=25\\t_{\alpha /2, (n-1)}=t_{0.01/2, (25-1)}=t_{0.005, 24}=2.797

    *Use the t-table for the critical value.

    Compute the 99% confidence interval as follows:

    CI=27.97\pm 2.797\times\frac{10.04}{\sqrt{25}}\\=27.97\pm5.616\\=(22.354, 33.586)\\\approx(22.35, 33.59)

    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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