Simple Random Sampling

To estimate a population proportion with a margin of error of ±0.05 at a 95% confidence level, and an estimated proportion of 0.5, what sample size is needed?

• 100

• 384

• 500

• 600

Answer explanation

If you want to estimate a population mean with a margin of error of 4, a population standard deviation of 20, and a 95% confidence level, what is the required sample size?

• 25

• 50

• 100

• 200

Answer explanation

A population consists of 1000 elements. You are to select a sample of 100 elements using simple random sampling without replacement. What is the probability of any single element being selected in the sample?

• 0.01

• 0.10

• 0.50

• 1.00

Answer explanation

The probability of any single element being selected in the sample is 0.10, which is calculated as the sample size (100) divided by the population size (1000), resulting in 0.10 or 10%.

A sample of 10 elements is selected without replacement from a population of 100 elements. What is the probability that a specific element is included in the sample?

• 0.01

• 0.05

• 0.10

• 0.50

Answer explanation

The probability of selecting the specific element is 1/100 = 0.01, as there are 100 elements in the population and only 1 specific element. Therefore, the correct answer is 0.01.

In a simple random sampling without replacement, which of the following is true about the sampling process?

• Each element has an equal probability of being selected, and the probability changes as elements are selected.

• Each element has a different probability of being selected, but the probability remains constant.

• Each element has an equal and constant probability of being selected.

• The elements are selected based on a predefined pattern.

Answer explanation

Each element has an equal probability of being selected, and the probability changes as elements are selected.

A sample of 200 people is taken from a population, and 60 people in the sample have a certain characteristic. What is the estimated proportion of the population with this characteristic?

• 0.20

• 0.25

• 0.30

• 0.40

Answer explanation

The estimated proportion of the population with the characteristic is calculated by dividing the number of people in the sample with the characteristic (60) by the total sample size (200), resulting in 0.30 or 30%.

If the true population mean (μ) is 50 and the population standard deviation (σ) is 10, what is the expected mean of the sample means (x̄) from all possible samples of size 25?

• 45

• 50

• 55

• 60

Answer explanation

The expected mean of the sample means (x̄) is equal to the population mean (μ), which is 50 in this case.

A sample of 40 students is taken from a population of 400 students. The sample mean is 70 with a standard deviation of 5. What is the standard error of the mean?

• 0.25

• 0.50

• 0.79

• 0.89

Answer explanation

The standard error of the mean is calculated by dividing the standard deviation by the square root of the sample size. In this case, it is 5 / sqrt(40) = 0.79.

In a simple random sampling with replacement, a sample of 5 is drawn from a population of 50. What is the probability of selecting a specific element (e.g., element A) at least once in the sample?

• 0.10

• 0.23

• 0.40

• 0.90

Answer explanation

The probability of not selecting the specific element in one draw is 49/50. Therefore, the probability of not selecting it in all 5 draws is (49/50)^5 ≈ 0.77. So, the probability of selecting it at least once is 1 - 0.77 = 0.23.

Given a sample proportion (p̂) of 0.6 from a sample of 150, what is the standard error of the sample proportion?

• 0.04

• 0.05

• 0.06

• 0.07

Answer explanation

The standard error of a sample proportion is calculated as sqrt((p̂*(1-p̂))/n), where p̂ = 0.6 and n = 150. Therefore, SE = sqrt((0.6*(1-0.6))/150) = 0.04.