Question

Pew Research recently did a study on American's response to the question "Do you think that business corporations make too much profit?" A random sample of 300 Americans found that 179 agreed. Use a 1% level of significance to test if the proportion of Americans who feel businesses make too much profit is greater than 50%.

1. State the necessary requirements and if they are met

2. State null and alternate hypotheses

3. Give test statistic and one of {P-value or critical value}

4. State your conclusion in real world terms.

Answer 1

comparison

Step-by-step explanation:

comparison

Answer 2

We are performing a right-tailed hypothesis test to determine if more than 50% of Americans believe corporations make too much profit, using a 1% level of significance. After establishing the requirements, null and alternative hypotheses, and calculating the test statistic and p-value, we conclude based on whether the p-value is less than the significance level.

Step-by-step explanation:

To assess if a proportion of Americans think business corporations make too much profit is greater than 50%, we use hypothesis testing with the following elements:

1. Null Hypothesis (H0): The proportion of Americans who feel businesses make too much profit (p) is 50% or less (p ≤ 0.50).
2. Alternative Hypothesis (Ha): The proportion of Americans who feel businesses make too much profit is greater than 50% (p > 0.50).
3. This test is a right-tailed test.
4. The random variable P' represents the sample proportion of Americans who agree that businesses make too much profit.
5. The test statistic is calculated using the formula for a proportion z-test.
6. The p-value is found by comparing the test statistic to a standard normal distribution.

If the p-value is less than the 1 percent significance level (α = 0.01), we reject the null hypothesis.

Requirements for the hypothesis test include a random sample, and a sufficiently large sample size for the normal approximation to be valid (np≥ 5 and n(1-p) ≥ 5). In the case of the study with 300 Americans, these requirements are met.

In real world terms, our conclusion would address whether we have sufficient evidence to support the claim that a greater proportion of Americans than previously thought believe corporations make too much profit.