Statistics Inferring and Sampling

What is the variance of the probability distribution?

• 2.18

• 2.19

• 2.20

• 2.21

Answer explanation

The correct answer is A. 2.18 as it matches the variance of the probability distribution provided in the question.

A randomly selected sample of 400 students at a university with 15-week semesters was asked whether or not they think the semester should be shortened to 14 weeks (with longer classes). Forty-six percent (46%) of the 400 students surveyed answered "yes." Which one of the following statements about the number 46% is correct?

• It is a sample statistic

• It is a random variable

• It is a population parameter

• It is a quantitative discrete variable

Answer explanation

The correct choice is C because 46% is a population parameter, representing the proportion of all students at the university who think the semester should be shortened.

What is "P(a<x<b)"?

• The area to the left of a.

• The area to the right of a.

• The area between a and b.

• The area to the right of b.

Answer explanation

The correct choice is C because 'P(a

What do you call a portion or representative of population?

• Parameter

• Population

• Sample

• Statistic

Answer explanation

A sample is a portion or representative of a population used to make inferences about the entire population.

Which of following is true about the mean of the sample means?

• The mean of the sample mean is equal to the population mean.

• The mean of the sample mean is equal to the population mean divided by the population variance.

• The mean of the sample mean is equal to the square of population mean.

• The mean of the sample mean is equal to the square root of population mean.

Answer explanation

The mean of the sample mean is equal to the population mean, making option A the correct choice.

Below are the scores of 8 Grade 11 students in the Statistics quiz. 7, 8, 12, 15, 10, 11, 9, 14
What is the mean of the sample means of size 3?

• 9.50

• 9.75

• 10.50

• 10.75

Answer explanation

The sample means of size 3 are (7+8+12)/3=9, (8+12+15)/3=11.67, (12+15+10)/3=12.33, (15+10+11)/3=12, (10+11+9)/3=10, (11+9+14)/3=11.33. The mean of these sample means is (9+11.67+12.33+12+10+11.33)/6=10.75, which is option D.

Which is NOT a correct statement?

• The total probability distribution of the sample mean is always equal to 1.

• There are 10 possible samples of size 3 drawn in the population N = 5.

• There are 31 possible samples of size 3 drawn in the population N = 7.

• There are 20 possible samples of size 3 drawn in the population N = 6.

Answer explanation

The correct statement is that there are 31 possible samples of size 3 drawn in the population N = 7, not 10 or 20.

Which concept of random sampling distribution of the sample means using Central Limit Theorem?

• If you have a population mean μ and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately distributed normally.

• The probability of the simultaneous occurrence of two events that are independent is given by the product of their individual probabilities.

• If you have a population mean μ and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately distributed same as the original population.

• The larger the sample size n in sampling distribution of sample mean, the lesser the histogram is to show the normalcy of the distribution.

Answer explanation

The correct choice is A because the Central Limit Theorem states that the distribution of sample means from a population will be approximately normally distributed with a large sample size.

What is the variance of the sample means of size 3 if the population variance is 6.9375?

• 1.5

• 1.6

• 1.7

• 1.8

Answer explanation

To find the variance of the sample means of size 3, divide the population variance by the sample size. 6.9375 / 3 = 1.5, therefore the correct answer is A. 1.5.

Human gestation length is said to be normally distributed with a mean of 266 days and a standard deviation of 16 days. Suppose 64 pregnancies are randomly selected. What is the probability that the average gestation length is between 262 and 270 days

• 95.45%

• 95.50%

• 95.75%

• 95.80%

Answer explanation

The probability of the average gestation length being between 262 and 270 days is 95.45%, which corresponds to choice A.