Each year, all final year students take a mathematics exam. It is hypothesised that the population mean score for this test is 80. It is kno

Question

Each year, all final year students take a mathematics exam. It is hypothesised that the population mean score for this test is 80. It is known that the population standard deviation of test scores is 13. A random sample of 23 students take the exam. The mean score for this group is 71. a)Calculate the 90% confidence interval for the population mean test score. Give your answers to 2 decimal places.

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Đan Thu 4 years 2021-09-04T16:54:20+00:00 1 Answers 19 views 0

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  1. diemthu
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    2021-09-04T16:56:12+00:00
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    Answer:

    The 90% confidence interval for the population mean test score is between 66.54 and 75.46.

    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 - 0.9}{2} = 0.05

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

    That is z with a pvalue of 1 - 0.05 = 0.95, so Z = 1.645.

    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 = 1.645\frac{13}{\sqrt{23}} = 4.46

    The lower end of the interval is the sample mean subtracted by M. So it is 71 – 4.46 = 66.54

    The upper end of the interval is the sample mean added to M. So it is 71 + 4.46 = 75.46

    The 90% confidence interval for the population mean test score is between 66.54 and 75.46.

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