Question

Suppose we want to compare the proportion of Texas residents (population 26 million) and the proportion of Wyoming residents (population 526 thousand) who have purchased items through online auction sites. We would like to select samples from each state in such a way that the sampling distributions have roughly equal variances. If the population proportions are nearly the same in each state, which one of the following statements is true?

A) Since the population sizes are so different, it's impossible to produce sample proportions whose sampling distributions have roughly the same variance.
B) Since the population sizes are random variables, we cannot estimate the variances of the sampling distributions.
C) The variances of the sampling distributions with be nearly the same if we sample the same percentage of residents from each state (for example, 0.5% of Texas residents and 0.5% of Wyoming residents).
D) The variances of the sampling distributions with be nearly the same if we sample a higher percentage of Texas residents to compensate for the larger population size.
E) The variances of the sampling distributions with be nearly the same if we sample the same number of residents of each state.

Answer 1

(c) the variance of the sampling distributions will be nearly the same if we sample the same percentage of residents from each state (for example, 0.5% of Texas residents and 0.5% of Wyoming residents.

Explanation:

Variance: the quality of being different or divergent.

Mathematically, Variance is the expectation of the squared deviation of a random variable from its mean