A leading CEO mentoring organization offers a program for chief executives, pres

Question

A leading CEO mentoring organization offers a program for chief executives, presidents, and business owners with a focus on developing entrepreneurial skills. Women and men executives that recently completed the program rated its value and the results are given in the accompanying table (marked Original Data). The chi-square procedures are not appropriate for the Original Data table because the expected counts are too small. However, by changing the table, an analysis can still be performed. We can often proceed after combining cell in some way that makes sense and also produce a table in which the conditions are satisfied. Both accompanying tables display the same data, but the second combines "Marginal" and "Poor" into a new category called "Below Average ". Are the perceptions of the program's value the same foe men and women? Complete parts a through c below. Click the icon to view the data tables. C. The expected cell counts are all less than 5. D. The expected cell counts are all greater than 5. State the null and alternative hypotheses. H_0: The distribution of responses about the value of the program for men and women executives is H_A: The distribution of responses about the value of the program for men and women executives is Determine the Chi^2 statistic. Chi^2 = (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) b) With this change in the table, what has happened to the number of degrees of freedom? A. The number of degrees of freedom decreased from 4 to 2. B. The number of degrees of freedom increased from 4 to 6 C. The number of degrees of freedom decreased from 4 to 3. D. The number of degrees of freedom increased from 4 to 5. c) Test the hypothesis about the CEO programs, and state an appropriate conclusion. H_0. There is evidence to support the alternative hypothesis that the distributions of responses about the value of the program for men and women executives are

Explanation / Answer

H0 : The distribution of responses ---------------- is same

Ha: The distribution of responses ---------------- is not same

2 = 17.660,     df = 3,     2/df = 5.89 ,         P(2 > 17.660) = 0.0005

warning:  some observed or expected frequencies are less than 5; thus the Central Limit Theorem may not apply and the resultant 2 may be invalid

expected values are displayed in italics
individual 2values are displayed in (parentheses)

DF for original data is (5-1)(2-1) = 4

DF for cmbined data is (4-1)(2-1) = 3

So reduced from 4 to 3

c)

Since p - value is less than 0.05, reject H0.

There is enough evidence to support the alternative that the distributions of responses about the value of theprogram for men and women are not same.

Men Women Excellent 3
8.18
( 3.28) 12
6.82
( 3.94) 15 Above Average 9
12.55
( 1.00) 14
10.45
( 1.20) 23 Average 16
12.00
( 1.33) 6
10.00
( 1.60) 22 Below Average 14
9.27
( 2.41) 3
7.73
( 2.89) 17 42 35 77

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