Question

which concept below is not a main idea of estimating a population proportion?
choose the correct answer below.
a. we can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion.
b. the sample proportion is the best point estimate of the population proportion.
c. using a sample statistic to estimate the population proportion is utilizing descriptive statistics.
d. knowing the sample size necessary to estimate a population proportion is important.

Explanation:

• Option A: Using a sample proportion to construct a confidence interval for the population proportion is a key concept in estimating population proportions. Confidence intervals give a range within which the true population proportion is likely to lie.
• Option B: The sample proportion \(\hat{p}\) is indeed the best point - estimate of the population proportion \(p\). A point - estimate is a single - value estimate of a population parameter.
• Option C: When we use a sample statistic (like the sample proportion) to estimate a population proportion, we are using inferential statistics, not descriptive statistics. Descriptive statistics summarize data (e.g., mean, median, proportion of a sample), while inferential statistics make inferences about a population based on sample data.
• Option D: Knowing the sample size is crucial. A larger sample size generally leads to more accurate estimates (narrower confidence intervals). The formula for the sample size \(n=\frac{z^{2}_{\alpha/2}\cdot p(1 - p)}{E^{2}}\) (where \(z_{\alpha/2}\) is the z - score, \(p\) is the estimated proportion, and \(E\) is the margin of error) is used to determine the necessary sample size.

Answer:

C. Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.