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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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Mathematics
3 years
2021-07-30T20:50:35+00:00
2021-07-30T20:50:35+00:00 1 Answers
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Answer:
The value of teh test statistic is![Rendered by QuickLaTeX.com z = 5.54](https://documen.tv/wp-content/ql-cache/quicklatex.com-e56a87ac8e7541c242fb74544c2ea2f2_l3.png)
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:
In which X is the sample mean,
is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.2 is tested at the null hypothesis:
This means that![Rendered by QuickLaTeX.com \mu = 0.2, \sigma = \sqrt{0.2*0.8} = 0.4](https://documen.tv/wp-content/ql-cache/quicklatex.com-a414f047d71eae6a300c5b6cabb0ae27_l3.png)
Using the sample results p^=0.27 with n=1003
This means that![Rendered by QuickLaTeX.com X = 0.27, n = 1003](https://documen.tv/wp-content/ql-cache/quicklatex.com-70f72e1a649ae8760d340cd43a18345c_l3.png)
Value of the test statistic:
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.