Question

In: Statistics and Probability

1. Students were asked whether they thought trust and honesty were essential in business and the...

1. Students were asked whether they thought trust and honesty were essential in business and the workplace. Here the counts classified by gender:

	Male	Female
Agree	11,724	14,169
Disagree	1,163	746

a. What percentage of females agreed?

b. What percentage of males agreed?

c. What is the explanatory variable?

d. Fill in the table of expected counts.

	Male	Female
Agree
Disagree

e. Fill in the table showing the calculation for each cell.

	Male	Female
Agree
Disagree

f. Find the total value.

g. Report the p-value.

h. At is there a significant association between gender and how one feels about the issue of whether or not trust and honesty are essential in business and the workplace? YES / NO

Solutions

Expert Solution

Percentage of females agreed = Number of females agree / Total number of females

= 14169 / (14169 + 746) = 0.95 = 95%

Percentage of males agreed = Number of males agree / Total number of males

= 11724 / (11724 + 1163) = 0.91 = 91%

The explanatory variable is Gender with 2 levels - Male and Female.

d and e.

The totals for each level are calculated as,

Total number of males = 11724 + 1163 = 12887

Total number of females = 14169 + 746 = 14915

Total agree = 11724+14169 = 25893

Total disagree = 1163+746 = 1909

Grand total = 25893 + 1909 = 27802

Expected counts for each cell is calculated as (Row total * Column Total) / Grand Total

	Male	Female	Total
Agree	(25893 * 12887)/ 27802 = 12002.13	(25893 * 14915)/ 27802 = 13890.87	25893
Disagree	(1909 * 12887)/ 27802 = 884.87	(1909 * 14915)/ 27802 = 1024.13	1909
Total	12887	14915	27802

Chi-square test statistc =

where Oi is the oberved count and Ei is the expected count for each cell.

Chi-square test statistc = (11724 - 12002.13)² / 12002.13 + (14169 - 13890.87)² / 13890.87 + (1163 - 884.87)² / 884.87 + (746 - 1024.13)² / 1024.13

= 174.9688

Degree of freedom = (row - 1) * (col - 1) = (2 - 1) * (2 - 1) = 1

P( > 174.9688) = 0

As, p-value is less than the significance level of 0.05, we conclude that there a significant association between gender and how one feels about the issue of whether or not trust and honesty are essential in business and the workplace. The answer is YES.

orchestra answered 1 year ago

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