Question 980123: The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He believes that the proportion of women in similar sales positions across the country is less than 45%. Hoping to find support for his belief, he directs you to test
H0: p .45 vs H1: p < .45.
In doing so, you collect a random sample of 50 salespersons employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women.
What is the smallest level of significance at which you could reject the null in favor of the alternative hypothesis?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is a one sample proportion test.
Ho p>=0.45
Ha p<0.45
alpha=0.05
Test statistic (phat-p) *se; se=sqrt {(0.45)(0.55)/50}=0.0704
Critical value at the 0.05 level is z=-1.645
Test stat=(0.36-0.45)/0.0704 =-1.278
p=0.1006
Fail to reject the null hypothesis at the 0.05 level.
The best that could be done is p<0.11, although it is very close to p=0.10
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