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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.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 $\alpha=.05$ .

a. $H_{0} : p \geq 0.24, H_{a} : p<0.24$b. $\hat{p}=0.2024$c. Fail to reject the null hypothesis $H_{0}$

Intro Stats / AP Statistics

Chapter 9

Hypothesis Tests

Confidence Intervals

Hypothesis Testing with One Sample

Hypothesis Testing with Two Samples

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in question 59. We're told that we have a population with a proportion of 0.24 and we're also given a more recent sample from the population in which the proportion is 81 out of 400 apart A. Whereas to set up a hypothesis test to determine whether the proportion has declined. The alternative hypothesis is that portion is less than 0.24 and the null hypothesis is that it is greater than or equal to 0.2 for for Party for Part B were asked, What is the point estimate of from portion. So our best point estimate of proportion is a sample proportion, which is 81 out of 400 and that equals 0.20 to 5. And then, for part C were asked Teoh test whether there has been a statistically significant decline in the proportion at a significance level of 0.5 So just blood these values into her test statistic that comes out to one minus 1.756 and so we can go to a standard normal table then and look up the area to the left of his escort my minus 1.756 This also happens to correspond to RP Valley because this is a lower tail test. So the P value is the area to the left of the test statistic. And so from the table, we can determine that the P value is equal to 0.392 and then to conclude, we can say that the P value is creator than Alfa and therefore we can fail to reject the null hypothesis.

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