Quizzol

QUESTION:

Which one of the following is true regarding the standard deviation of the sampling distribution of the sample proportion, p-hat, of "yes" responses?

The standard deviation of the sampling distribution will be 9 times smaller with sample size 100.

The standard deviation of the sampling distribution will be 9 times larger with sample size 100.

The standard deviation of the sampling distribution will be 3 times smaller with sample size 100.

The standard deviation of the sampling distribution will be 3 times larger with sample size 100.

The standard deviation of the sampling distribution will be the same for both sample sizes.

ANSWER:

The standard deviation of the sampling distribution will be 3 times larger with sample size 100.

For a sample size of 100, the sampling distribution of p-hat is:

\sqrt{\frac{p (1 - p)}{100}}

. For a sample of size 900, the sampling distribution of p-hat is:

\sqrt{\frac{p (1 - p)}{900}}

. This is the correct answer since:

\sqrt{\frac{p (1 - p)}{900}}

\sqrt{\frac{p (1 - p)}{9 * 100}}

\frac{1}{3} \sqrt{\frac{p (1 - p)}{100}}

Posted by Cleveland on September 22, 2024