A fast food restaurant executive wishes to know how many fast food meals teenagers eat each week. They want to construct a 99% confidence in

Question

A fast food restaurant executive wishes to know how many fast food meals teenagers eat each week. They want to construct a 99% confidence interval with an error of no more than 0.06. A consultant has informed them that a previous study found the mean to be 6.4 fast food meals per week and found the standard deviation to be 1.1. What is the minimum sample size required to create the specified confidence interval

in progress 0
Alexandra 4 weeks 2021-09-20T13:37:50+00:00 1 Answer 0

Answers ( )

    0
    2021-09-20T13:38:54+00:00

    Answer:

    The minimum sample size required to create the specified confidence interval is 2229.

    Step-by-step explanation:

    We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

    \alpha = \frac{1-0.99}{2} = 0.005

    Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

    So it is z with a pvalue of 1-0.005 = 0.995, so z = 2.575

    Now, find the margin of error M as such

    M = z*\frac{\sigma}{\sqrt{n}}

    In which \sigma is the standard deviation of the population and n is the size of the sample.

    What is the minimum sample size required to create the specified confidence interval

    This is n when M = 0.06, \sigma = 1.1

    0.06 = 2.575*\frac{1.1}{\sqrt{n}}

    0.06\sqrt{n} = 2.575*1.1

    \sqrt{n} = \frac{2.575*1.1}{0.06}

    (\sqrt{n})^{2} = (\frac{2.575*1.1}{0.06})^{2}

    n = 2228.6

    Rounding up

    The minimum sample size required to create the specified confidence interval is 2229.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )