You are the head of the neighborhood council in your community. The council is planning a Family Week event and decides to survey people around the neighborhood about what activities to include in the event. You divide the council into two groups. Team A surveys 50 people, while Team B surveys 200 people. Both teams present their data in a sampling distribution. Taking their data into account, which of the following statements best describes the data they collect?(1 point)

Question

Responses

The mean of the sample distribution of Team B will approximate the population proportion of Team A.
The mean of the sample distribution of Team B will approximate the population proportion of Team A.

The graphical representation of Team A’s data will look more symmetric than that of Team B.
The graphical representation of Team A’s data will look more symmetric than that of Team B.

The mean of the sample distribution of size 50 will approximately equal the population proportion of the data gathered by Team A.
The mean of the sample distribution of size 50 will approximately equal the population proportion of the data gathered by Team A.

The data of Team A has less variability than that of Team B.

Answer 1

The correct statement that best describes the data collected by Team A and Team B is:

The mean of the sample distribution of size 50 will approximately equal the population proportion of the data gathered by Team A.

Here's why:

• Both Team A and Team B are collecting sample data, and the means of their sampling distributions will approximate the true population proportion as the sample size increases. While Team B has a larger sample size (200 compared to Team A's 50), both teams' sample means should approximate their respective population proportions.

• The statement about the graphical representation of Team A’s data looking more symmetric than that of Team B is unlikely to be accurate, as larger sample sizes typically produce distributions that approach normality due to the Central Limit Theorem, leading to more symmetric distributions.

• The mention of Team A's data having less variability than Team B is incorrect since a smaller sample typically exhibits more variability than a larger one, all else being equal.

Thus, focusing on the approximation of the sampling distribution's mean to the population proportion is the most accurate reflection of the scenario described.