Question

A population proportion is 0.5. A simple random sample of size 64 will be taken, and the sample proportion p will be used to estimate the population proportion. What is the probability that the sample proportion will be within +/- 0.05 of the population proportion?

a) 0.95
b) 0.90
c) 0.99
d) 0.80

Answer 1

The probability that the sample proportion will be within +/- 0.05 of the population proportion is a) 0.95.

Step-by-step explanation:

To find the probability that the sample proportion will be within +/- 0.05 of the population proportion, we need to calculate the sampling error. The sampling error is the difference between the sample proportion and the population proportion. In this case, the population proportion is 0.5 and the sample size is 64.

The sampling error can be calculated using the formula:

Sampling error = (p - p') / sqrt((p*(1-p))/n)

Where p is the population proportion, p' is the sample proportion, n is the sample size.

Substituting the given values, we get:

Sampling error = (0.5 - p') / sqrt((0.5*(1-0.5))/64)

The probability that the sample proportion will be within +/- 0.05 of the population proportion can be calculated by finding the Z-scores associated with the sampling error and using the Z-table.

Since the Z-scores associated with a probability of 0.025 on each tail of the distribution encompass a 95% confidence level, the probability that the sample proportion will be within +/- 0.05 of the population proportion is a)0.95.