Statistics Inferring and Sampling

What is the probability that corresponds to the z > -0.33?

• 0.3707

• 0.6293

• 0.7293

• 0.2707

Answer explanation

The probability corresponding to z > -0.33 is the area to the right of -0.33 on the standard normal distribution curve, which is 0.6293.

If the population standard deviation of a dataset is 2.4, what is the population variance?

• 1.55

• 5.76

• 1.33

• 4.8

Answer explanation

To find the population variance, square the standard deviation. Therefore, 2.4^2 = 5.76. Hence, the population variance is 5.76.

If the population variance of a set of data is 28.36, what is the population standard deviation?

• 4.33

• 5.33

• 6.33

• 7.33

Answer explanation

To find the population standard deviation, take the square root of the population variance. √28.36 = 5.33, so the correct answer is 5.33.

If the population standard deviation of a dataset is 1.9, what is the population variance?

• 1.38

• 3.61

• 3.8

• 0.95

Answer explanation

To find the population variance, square the standard deviation. Therefore, 1.9^2 = 3.61. Hence, the population variance is 3.61.

If the population mean is 3.7, what is the mean of the sampling distribution?

• 3.7

• 1.92

• 13.69

• 0

Answer explanation

The mean of the sampling distribution is equal to the population mean, so it is 3.7. Therefore, the correct choice is 3.7.

If the dataset has a sample size of n=3 with a population variance of 11.43, what is the variance of the sampling distribution of the means?

• 2.81

• 3.81

• 4.81

• 5.81

Answer explanation

The variance of the sampling distribution of the means is population variance divided by sample size, 11.43/3 = 3.81. Therefore, the correct answer is 3.81.

If the dataset has a sample size of n=4 with a population standard deviation of 4.84, what is the standard deviation of the sampling distribution of the means?

• 2.2

• 2.42

• 2.22

• 2.24

Answer explanation

The standard deviation of the sampling distribution of the means is calculated as population standard deviation divided by the square root of the sample size. Therefore, it is 4.84 / sqrt(4) = 2.42.

What is the first step in finding the variance of a discrete probability distribution?

• Calculate the standard deviation

• Find the mean of the probability distribution

• Subtract the mean from each value of the random variable X

• Multiply the square of the difference of X and the mean by each value of the random variable.

Answer explanation

The first step in finding the variance of a discrete probability distribution is to find the mean of the probability distribution.

The expected value of a random variable is the

• largest value that will ever occur.

• mean value over an infinite number of observations of the variable.

• most common value over an infinite number of observations of the variable.

• value that has the highest probability of occurring.

Answer explanation

The expected value of a random variable is the mean value over an infinite number of observations of the variable, making option B the correct choice.

Which statement is NOT true about the variance of a discrete random variable?

• Variance is always nonnegative.

• It tells the average of the items in a discrete probability distribution

• It measures how far apart the elements of the set are spread out

• High variance indicates that the data points are very spread out around the mean.

Answer explanation

The correct statement is B. Variance does not tell the average of the items in a discrete probability distribution, but rather measures the spread of the data points.