according to the federal government 24 of workers covered by

according to the federal government, 24% of workers covered by their company\'s health care plan were not required to contribute to the premium. A recent study found that 81 out of 400 workers sampled were not required to contribute to thier company\'s health care plan.

A. Develop hypotheses that can be used to test whether the percent of workers not required to contribute to thier company\'s health care plan has declined.

ho:p--

ha:p--
B. What is a point estimate of the proportion receiving free company-sponsored health care insurance? 4 decimals

C. has a statistically significally decline occured in the proportion of workers receiving free company-sponsored health care insurance? Use a = .05

calculate the value of the test statistic 2 decimals.

what is the p value 4 decimals.

what is your conclusion.

Solution

pp = population proportion
sp = sample proportion
n = sample size
pq = 1 - pp
se = standard error = sqrt((pp*pq)/n)

in your problem:

pp = .24
pq = 1 - .24 = .76
sp = 81/400 = .2025
n = 400
se = sqrt ((.24*.76)/400) = .021354

z = z-score = (sp - pp) / se

in your problem:

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).