A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was selected of 10 one-bedroom units wi

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A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was selected of 10 one-bedroom units within a half-mile of campus and the rents paid. The sample mean is $550 and the sample standard deviation is $60.05. Provide a 95% confidence interval estimate of the mean rent per month for the population of one-bedroom units within a half-mile of campus. Assume that population is normally distributed.

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  1. Answer:

    (507.05, 592.95)

    Step-by-step explanation:

    Given data:

    sample mean = $550, sample standard deviation S = $60.05

    95% confidence interval , n = 10

    For 95% confidence interval for the mean

    mean ± M.E.

    where M.E. is margin of error = [tex]t_{n-1}, \alpha/2\times\frac{S}{\sqrt{n} }[/tex]

    Substituting the values in above equation

    [tex]=t_{10-1}, 0.05/2\times\frac{60.05}{\sqrt{10} }[/tex]

    = 2.62×18.99

    =42.955

    = 550±42.95

    =(507.05, 592.95)

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