Chapter 10 %28pages 139-152%29

# Chapter 10 %28pages 139-152%29 - MSIT 3000 Chapter 10...

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MSIT 3000 Chapter 10 Testing Hypotheses about Proportions A study was done to see if bank executives were more inclined to promote males than females. Forty-eight randomly chosen bank executives were given a resume of a fictitious candidate and asked if they would promote the given candidate to a management position. The 48 resumes were identical except 24 had male names and 24 had females names. Thirty-five executives said they would promote the given candidate to a management position. However, of these 35 who would be promoted, 21 were male and only 14 were female. Does this provide evidence of discrimination? YES or NO?? 139

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Assuming no discrimination against females, bank executives would be equally likely to promote either gender. The proportion of females who were recommended is 14/35 = 0.4, which is less than 0.5… but is it far enough from 0.5 to cast doubt on the initial assumption of no discrimination? Even though the 48 resumes were identical, only 35 were recommended for promotion. Could the reason be something other than discrimination? Would a different random sample of executives produce a proportion of recommended females closer to 0.5? In other words, how sure can we be that the observed 0.4 is due to discrimination rather than randomness? We need a formal statistical procedure to decide. 140
MSIT 3000 Section 10.1: Hypotheses Hypothesis Test for a Single Proportion 1. Hypotheses: H 0 : p = p 0 H a : p < p 0 left-tailed test H a : p > p 0 right-tailed test H a : p ≠ p 0 two-tailed test 2. Model: Random sample, 10% condition, and, both np 0 10 and nq 0 10. 3. Mechanics a. z = 0 0 0 ˆ p p p q n - test statistic b. Find probability (p-value*) using normal model 4. Conclusions: If P-value α , reject H 0 . There is sufficient evidence, at α , H a is true. If P-value > α , fail to reject H 0 . There is not sufficient evidence, at α , H a is true. *A HT asks, "Could these data plausibly have happened by chance if the null hypothesis were true?” This is the probably represented by a p-value. 141

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Ex : A consulting firm had predicted that 35% of the employees at a large firm would take advantage of a new company credit union, but management is optimistic. They think the rate is higher. A survey of 300 employees shows that 128 of them are currently taking advantage of the Credit Union. Is the proportion of employees who use the Credit Union higher than the consulting firm predicted? Use α = 0.05. a. State hypotheses
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Chapter 10 %28pages 139-152%29 - MSIT 3000 Chapter 10...

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