P3: According to the federal government, 24% of workers covered by their company
ID: 3314556 • Letter: P
Question
P3: 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: 2000). A recent study found that 81 out of 400 workers sampled were not required to contribute to their company's health care plan. 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 2. What is a point estimate of the proportion receiving free company-sponsored health care insurance? 3. Has a statistically significant decline occurred in the proportion of workers receiving free company-sponsored health care insurance? Use a .05.Explanation / Answer
1) here null hypothesis: Ho: p >=0.24
alternate hypothesis: Ha: p<0.24
2)point estimate phat =81/400=0.2025
3)here for 0.05 level and left tailed test ; critical value of z =-1.645
Deciision rule: reejct Ho if test statistic z<-1.645
for p=0.24 and n=400
std error =(p*(1-p)/n)1/2 =0.0214
therefore test statsitic z=(phat-p)/std error =(0.2025-0.24)/0.0214=-1.7561
as test statistic is lower from critical value ;w e reject null hypothesis
and conclude at 0.05 level that a statisically singificant declined occured in the proportion..............
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