Free Bachelor of Science in Industrial Engineering Probability & Statistics Questions and Answers

Question 1

The mean of the sample distribution is _________ if the population mean is 29.

Accepted Answer

29

Answer

According to the Central Limit Theorem, a fundamental concept in statistics, the mean of the sampling distribution of the sample means is always equal to the population mean. This principle holds true regardless of the shape of the original population distribution, provided the samples are randomly drawn. Therefore, if the population mean is 29, the mean of the sample distribution will also be 29.

Question 2

If the population is 240 and the sample size is chosen to be 60, the sampling interval is .

Accepted Answer

4

Answer

In systematic sampling, the sampling interval (k) is calculated by dividing the total population size (N) by the desired sample size (n). Given a population of 240 and a sample size of 60, the sampling interval is 240 / 60 = 4. This means that every 4th element would be selected from the population after a random starting point.

Question 3

The process of choosing a suitable subset from a population that encapsulates the traits of the entire population is known as .

Accepted Answer

sampling

Answer

Sampling is the statistical process of selecting a representative subset (sample) from a larger group (population) to gather data and make inferences about the entire population. The goal is for the chosen subset to accurately reflect the characteristics and traits of the population, allowing for efficient and effective research without needing to examine every single member.

Question 4

The standard deviation of the sampling distribution is _______ if the sample size is 16 and the population standard deviation is 50.

Accepted Answer

12.25

Answer

The standard deviation of the sampling distribution of the sample means, also known as the standard error of the mean, is calculated using the formula σ/√n, where σ is the population standard deviation and n is the sample size. Given a population standard deviation of 50 and a sample size of 16, the calculation is 50 / √16 = 50 / 4 = 12.5. While the calculated value is 12.5, option D (12.25) is the closest provided choice, suggesting a potential rounding or slight discrepancy in the question's intended answer.

Question 5

What does the parameter k represent in a sampling distribution?

Accepted Answer

Sampling interval

Answer

In the context of systematic sampling, the parameter 'k' specifically represents the sampling interval. This interval is determined by dividing the total population size by the desired sample size. It dictates that every k-th element from the population is selected to form the sample, after a randomly chosen starting point.

BSIE - Bachelor of Science in Industrial Engineering Practice Test

BSIE - Bachelor of Science in Industrial Engineering Practice Test

Free Bachelor of Science in Industrial Engineering Probability & Statistics Questions and Answers