According to the federal government, 24 % of workers covered...

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 bealth 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 $a-.05$.

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 bealth 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 $a-.05$.

Key Concepts

Significance Level

The significance level, denoted by alpha (?), is the threshold for determining whether the observed results are statistically significant. It represents the probability of rejecting the null hypothesis when it is actually true (Type I error). In this context, an ? of 0.05 is used, meaning there is a 5% risk of concluding there is a decline in the proportion when there is none.

Point Estimation

Point estimation involves calculating a single value from sample data to estimate a population parameter. In problems involving proportions, the sample proportion (number of successes divided by sample size) serves as the point estimate for the true proportion in the population.

Hypothesis Testing

Hypothesis testing is a statistical method used to decide if there is enough evidence to support a claim about a population parameter. It involves formulating a null hypothesis that represents the status quo and an alternative hypothesis that reflects the claim to be tested, computing a test statistic from sample data, and comparing it to a critical value or using a p-value to make a decision.

Null and Alternative Hypotheses

The null hypothesis (H0) typically states that there is no change or effect—in this case, that the current proportion of workers receiving free health care insurance is equal to the previously reported proportion. The alternative hypothesis (H1) is the claim being tested, which here posits that the proportion has declined from the government’s reported value.

Transcript

Please give Ace some feedback