We would like to estimate the true mean number of hours adults sleep at night. Suppose that sleep time is known to follow a Normal distribut

Question

We would like to estimate the true mean number of hours adults sleep at night. Suppose that sleep time is known to follow a Normal distribution with standard deviation 1.5 hours. For a sample of 12, what is the margin of error for a 95% confidence interval

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Arya 2 weeks 2021-09-12T01:31:03+00:00 1 Answer 0

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    2021-09-12T01:32:50+00:00

    Answer:

    The margin of error for a 95% confidence interval is 0.8487 hours of sleep.

    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{1-0.95}{2} = 0.025

    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 1-0.025 = 0.975, so z = 1.96

    Now, we 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.

    For a sample of 12, what is the margin of error for a 95% confidence interval

    M = 1.96*\frac{1.5}{\sqrt{12}} = 0.8487

    The margin of error for a 95% confidence interval is 0.8487 hours of sleep.

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