Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random

Question

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5% significance level.
Test H0 : p=0.2 vs Ha : p≠0.2 using the sample results p^=0.27 with n=1003
Round your answer for the test statistic to two decimal places, and your answer for the p-value to three decimal places.

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Diễm Kiều 4 years 2021-07-30T20:50:35+00:00 1 Answers 60 views 0

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  1. King
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    2021-07-30T20:51:43+00:00
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    Answer:

    The value of teh test statistic is z = 5.54

    The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that the proportion differs from 0.2.

    Step-by-step explanation:

    The test statistic is:

    z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

    In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

    0.2 is tested at the null hypothesis:

    This means that \mu = 0.2, \sigma = \sqrt{0.2*0.8} = 0.4

    Using the sample results p^=0.27 with n=1003

    This means that X = 0.27, n = 1003

    Value of the test statistic:

    z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

    z = \frac{0.27 - 0.2}{\frac{0.4}{\sqrt{1003}}}

    z = 5.54

    P-value of the test and decision:

    The p-value of the test is the probability that the sample proportion differs from 0.2 by at least 0.07, which is P(|z| > 5.54), that is, 2 multiplied by the p-value of z = -5.54.

    Looking at the z-table, z = -5.54 has a p-value of 0.

    2*0 = 0.

    The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that the proportion differs from 0.2.

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