Suppose you asked 100 commuters how much they spend each year and obtained a mean of $167 spent on transportation and a standard deviation o

Question

Suppose you asked 100 commuters how much they spend each year and obtained a mean of $167 spent on transportation and a standard deviation of $40. Using the 2 SE rule of thumb, calculate a 95% confidence interval for the mean and select the values that come closest to those that would fill the spaces in the following interpretation: we can be 95% confident that the mean amount of money spent on transportation lies between _________ and _________.A. $149 and $185 B. $163 and $171 C. $163 and $170 D. $155 and $212

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Adeline 3 weeks 2021-09-10T08:16:44+00:00 1 Answer 0

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    2021-09-10T08:17:57+00:00

    Answer:

    B. $163 and $171

    Step-by-step explanation:

    from the question, we were given the following:

    mean= $167

    standard deviation, =$40

    sample size, n = 100

    significance level, α= i- confidence level= 1- 0.95=0.05

    from the z table, we get;

    critical value, Z_{\alpha/2 }  = Z_{0.025} = 1.96

    error margin = critical value ×\frac{standard \ deviation}{\sqrt{sample\ size} }

                         = 1.96×\frac{40}{\sqrt{100} } = 7.84

    thus lower limit = mean – error margin = $167 – $7.84 =159.16

    the upper limit = mean + error margin = $167 + $7.84 = $174.84

    the closest is B. $163 and $171

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