Consider Sampling from a Population Whose Proportion of Successes Is $\hat{p}$

question 2

Essay

Consider sampling from a population whose proportion of successes is p = 0.5. Asthe sample size, n, increases, some characteristics of the sampling distribution ofchange. Which of the following characteristics will change as n increases, and whatis the nature of the change?
a) The mean of the sampling distribution of $\hat{p}$
b) The standard deviation of the sampling distribution of $\hat{p}$
c) The shape of the sampling distribution of $\hat{p}$

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Definitions:

Normal Distribution

The normal distribution, often called the Gaussian distribution, is a bell-shaped curve that describes the spread of a characteristic throughout a population where most occurrences take place around the average value.

Positively Correlated

A relationship between two variables where both variables move in tandem, meaning that when one variable increases, the other does as well.

Negatively Correlated

A relationship between two variables in which one variable increases as the other decreases, and vice versa.

Zero Correlation

A statistical term indicating no relationship between two variables, meaning that changes in one do not predict changes in the other.