Summative Test in Statistics and Probability

Which of the following values do we need to define the sampling distribution?

• probability

• standard deviation

• Statistic

• parameter

How can the standard error be reduced in surveys?

• by decreasing the population size

• by decreasing the sample size

• by increasing the sample size

• by increasing the population size

The average lot size of the houses in a small village is 55 square meters with a standard deviation of 10 square meters. Find the mean of the sampling distribution of the sample mean with a sample size of 50 houses if lot sizes are normally distributed.

• 10

• 50

• 55

• 60

Find the standard error of the sampling distribution of the sample mean if n=75 and σ=500.

• 57.74

• 425

• 6.67

• 0.3

A normal population has a mean of 100. Find the standard error of the sampling distribution of the sample mean of a normal population with a sample size of 100 if the population standard deviation is equal to 10% of the population mean.

• 1

• 100

• 10

• 0.1

Which of the following is true about the mean of the sampling distribution of the sample mean if the population mean is unknown?

• It is approximately equal to the mean of a single sample.

• It is approximately equal to the mean of a single sample divided by the sample size.

• It is equal to the mean of a single sample divided by the sample size.

• It is equal to the mean of a single sample.

What is in the center of the sampling distribution?

• true sample mean

• variance

• standard deviation

• true population mean

A shipping company measured the weight of a sample of 50 boxes in its warehouse. The average weight of the boxes is 25 kg with a standard deviation of 12 kg. Estimate the mean of the sampling distribution of the sample mean if the weights follow a normal distribution.

• 25 kg

• 1250 kg

• 1.7 kg

• 12 kg

What is the standard error of the mean if a sample of 400 units has a mean of 15 and a standard deviation of 2? Assume that the population is normally distributed.

• 0.13

• 0.005

• 15

• 0.1

Four students took an exam in mathematics and got the following scores: 7, 12, 19, and 21. What is the mean of the sampling distribution of the sample mean with a sample size of 2?

• 14.75

• 14.5

• 13.75

• 13.5