SOLUTION: According to the federal government, 24% of workers covered by their company's health care plan were not required to contribute to the premium (Statistical Abstract of the United S
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Question 852037: According to the federal government, 24% of workers covered by their company's health care plan were not required to contribute to the premium (Statistical Abstract of the United States: 2006). A recent study found that 81 out of 400 workers sampled were not required to contribute to their company's health care plan.
a. Develop hypotheses that can be used to test whether the percent of workers not required to contribute to their company's health care plan has declined.
H0: p _________________
Ha: p _________________
b. What is a point estimate of the proportion receiving free company sponsored health care insurance?
c. Has a statistically significant decline occurred in the proportion of workers receiving free company sponsored health care insurance? Use alpha= 0.05 Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! pp = population proportion
sp = sample proportion
n = sample size
pq = 1 - pp
se = standard error = sqrt((pp*pq)/n)
z = (.2025 - .24) / .021354 which is equal to -1.756111
since you are looking for whether the ratio has declined, this is a one tailed test at .05 alpha.
you are looking for the proportion of the normal distribution curve that has a z-score less than -1.75611.
the z-score table tells you that this ratio is .039535.
since this is less than than than the stated alpha of .05, the results are statistically significant.
the answers to your questions are:
a. Develop hypotheses that can be used to test whether the percent of workers not required to contribute to their company's health care plan has declined.
H0: p ____= .24_____________
Ha: p ____< .24_____________
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b. What is a point estimate of the proportion receiving free company sponsored health care insurance?
sp = sample proportion = .2025
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c. Has a statistically significant decline occurred in the proportion of workers receiving free company sponsored health care insurance? Use alpha= 0.05
yes (.039535 is smaller than .05, therefore the results are significant).
a good reference on how to do a hypothesis on a proportion can be found at the following link:
