The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval fo

Question

The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds.a. Construct a 95% confidence interval for the population mean weight of newborn elephants. State the confidence interval. (Round your answers to two decimal places.)

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Jade 1 week 2021-09-15T14:45:52+00:00 1 Answer 0

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    2021-09-15T14:47:39+00:00

    Answer:

    The 95% confidence interval for the population mean weight of newborn elephants is between 242.12 pounds and 245.88 pounds.

    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, find 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 = 1.96*\frac{15}{244} = 1.88

    The lower end of the interval is the sample mean subtracted by M. So it is 244 – 1.88 = 242.12 pounds.

    The upper end of the interval is the sample mean added to M. So it is 244 + 1.88 = 245.88 pounds

    The 95% confidence interval for the population mean weight of newborn elephants is between 242.12 pounds and 245.88 pounds.

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