MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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leaders attending a large national leadership conference and that 53 were found to be extroverts. Does this indicate that the population proportion of extroverts among college student government leaders is different (either way) from 79%? Use ? = 0.01.
(a) What is the level of significance?
State the null hypothesis
(b) What sampling distribution will you use?
and nq
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
(e) Interpret your conclusion in the context of the application.
State the null hypothesis
H0
and the alternate hypothesis
H1
.H0
: p H1
: p (b) What sampling distribution will you use?
The Student's tThe standard normal
since np and nq
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude that the true proportion of extroverts among college student government leaders differs from 79%.There is insufficient evidence at the 0.01 level to conclude that the true proportion of extroverts among college student government leaders differs from 79%.
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