4) The Law School Admission Test (LSAT) is an examination for prospective law school students. Scores on the LSAT are known to have a normal

Question

4) The Law School Admission Test (LSAT) is an examination for prospective law school students. Scores on the LSAT are known to have a normal distribution and a population standard deviation of σ = 10. A random sample of 250 LSAT takers produced a sample mean of 502. Compute a 99% confidence interval for the population mean LSAT score. Show all work, and round all decimals that you use to three decimal places.

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Natalia 3 hours 2021-09-15T00:26:32+00:00 1 Answer 0

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    2021-09-15T00:27:58+00:00

    Answer:

    The 99% confidence interval for the population mean LSAT score is between 500.371 and 503.629

    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.

    M = 2.575\frac{10}{\sqrt{250}} = 1.629

    The lower end of the interval is the sample mean subtracted by M. So it is 502 – 1.629 = 500.371

    The upper end of the interval is the sample mean added to M. So it is 502 + 1.629 = 503.629

    The 99% confidence interval for the population mean LSAT score is between 500.371 and 503.629

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