MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:One strategy that may have an impact on employee retention, turnover and engagement is a successful employee recognition program. Surveying small organizations, those with 500 to 2,499 employees, and large organizations, those with 10,000 or more employees, a survey organization showed that 312 (73%) of the 426
small organizations have employee retention programs as compared to 175 (83%) of the 210 large organizations. Complete parts (a) through (c) below.
a. At the 0.05 level of significance, is there evidence of a significant difference between organizations with 500 to 2,499 employees and organizations with 10,000 or more employees with respect to the proportion that have employee recognition programs?
Let group 1 be the organizations with 500 to 2,499 employees, and let group 2 be the organizations with 10,000 or more employees. State the null and alternative hypotheses. Choose the correct answer below.
O A. Ho: > T2
O B. Ho: sA2
H,: , > 12
OC. Ho: , 2 T2
O D. Ho: a, = T2
O E. Ho: 1 <2
OF. Ho: 1 2
Calculate the test statistic.
(Round to three decimal places as needed.)
Determine the critical value.
The critical value is.
(Round to three decimal places as needed.)
State the conclusion.
the null hypothesis. There is
evidence at the 0.05 level of significance to conclude that there is a significant difference between organizations with 500 to 2,499 employees and organizations with 10,000 or more employees with respect to the proportion that have employee retention programs
b. Find the p-value in (a) and interpret its meaning.
The p-value is.
(Round to three decimal places as needed.)
Interpret the p-value.
The probability of obtaining a difference in proportions that gives rise to a test statistic
the
is equal to the p-value if there is no difference between the population proportions of organizations with 500-2,499 employees and organizations with 10,000 or more employees
that have employee retention programs.
C. An earlier Z-test for the difference between two proportions in part (a) resulted in a test statistic of ZSTAT = - 2.83 against critical values of - 1.96 and 1.96, with a p-value of 0.005. Compare the results of (a) and (b) to the results of the Z-tests.
O A. Both tests agree that the null hypothesis should not be rejected.
O B. The chi-square test concluded that the null hypothesis should not be rejected, while the Z-test concluded that the null hypothesis should be rejected.
OC. Both tests agree that the null hypothesis should be rejected.
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