Question

12. The mean of a distribution of sample proportions is 0.13, and the standard error is 0.02. What two values will 95% of the sample

proportions fall between?

Answer choices:
0.11 and 0.15
0,09 and 0.17
0.07 and 0.19
0.05 and 0 21

Answer 1

The answer is (B) 0.09 and 0.17.

Explanation:

We can use the formula for the confidence interval for a population proportion to find the two values that 95% of the sample proportions will fall between:

sample proportion +/- z* (standard error)

where z* is the z-score corresponding to the desired level of confidence (in this case, 95%).

Using a standard normal distribution table or calculator, we can find that the z-score for a 95% confidence level is approximately 1.96.

Substituting the given values into the formula, we have:

0.13 +/- 1.96(0.02)

Simplifying, we get:

0.13 +/- 0.0392

So the 95% confidence interval for the population proportion is (0.0908, 0.1692).

Therefore, the two values that 95% of the sample proportions will fall between are 0.09 and 0.17.

The answer is (B) 0.09 and 0.17.