Question

A recent Gallup Poll asked 4045 randomly chosen American adults to rate the ethical standards of 45 occupations. Nurses were at the top, with 73% of the poll respondents rating them very high. Identify the following:

(a) What is the population of interest for this study?
(b) What is the sample for this study?
(c) Is the number 73% considered a parameter or a statistic? Explain.
(d) How many of the 4045 American adults in the Gallup poll rated nurses with very high ethical standards?
(e) Estimate the margin of error for this poll using 95% confidence. Round to two decimal places as necessary.
(f) Give the 95% confidence interval for this poll.
(g) Make a confidence statement about this poll in context.

Answer 1

The study's population of interest is all American adults, the sample is the 4045 American adults who were polled, and the 73% is a statistic of the sample. Approximately 2953 American adults rated nurses very highly. Margin of error and 95% confidence interval cannot be calculated accurately without additional data such as standard deviation.

Step-by-step explanation:

To address the student's questions regarding the Gallup Poll:

1. Population of interest: It is the entire group of American adults from whom the poll seeks to understand the ethical standards of various occupations.
2. Sample: The 4045 randomly chosen American adults who participated in the Gallup Poll.
3. The number 73% is considered a statistic, as it is a measure calculated from the sample of 4045 American adults and it estimates a parameter of the population.
4. To find how many rated nurses with very high ethical standards, multiply 4045 by 0.73 to get 2952.85, which, when rounded, indicates that approximately 2953 American adults rated nurses very highly.
5. Regarding the margin of error for this poll at 95% confidence, assuming a standard normal distribution (Z-score of 1.96 for 95% confidence), the formula MOE = Z ∙ sqrt[(p(1-p)/n)] can be applied, where p is the sample proportion (0.73) and n is the sample size (4045).
6. Since exact calculation of the margin of error requires further details like the standard deviation, a precise MOE here cannot be provided without more information.
7. 95% confidence interval and confidence statement would also depend on the margin of error, which we do not have the necessary data for in this scenario to calculate accurately.