In one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x ?

Approximately normal with mean 5.5 days and standard deviation 0.26 day

Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 days

Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 day

Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 day

Approximately normal with mean 5.5 days and standard deviation 2.6 days

Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?

A sample of size 25 will produce more variability of the estimator than a sample of size 50.

A sample of size 25 will produce less variability of the estimator than a sample of size 50.

A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.

A sample of size 25 will produce a more biased estimator than a sample of size 50.

A sample of size 25 will produce a less biased estimator than a sample of size 50.

A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer’s batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem?

The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.

The distribution of the number of recharge cycles for the sample is approximately normal because the population mean of 400 is greater than 30.

The distribution of the number of recharge cycles for the sample is approximately normal because the sample size of 100 is greater than 30.

The distribution of the number of recharge cycles for the population is approximately normal because the sample size of 100 is greater than 30.

The distribution of the sample means of the number of recharge cycles is approximately normal because the population mean of 400 is greater than 30.

At a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

78% is a parameter and 72% is a statistic

78% is a population and 72% is a sample.

72% is a population and 78% is a sample

72% is a parameter and 78% is a statistic

Sampling Distributions

Authored by Masha Stine

Mathematics

12th Grade

CCSS covered

Used 10+ times

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let p-hat be the proportion of people in the sample who attended church. A newspaper report claims that 40% of all U.S. adults went to church last week. Suppose this claim is true.
What is the mean of the sampling distribution of p-hat?

0.4

0.44

0.56

0.6

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let p-hat be the proportion of people in the sample who attended church. A newspaper report claims that 40% of all U.S. adults went to church last week. Suppose this claim is true.
Calculate the standard deviation of the sampling distribution.

0.0116

0.0117

0.0118

0.0119

What happens to the shape of a sampling distribution of sample proportions as n increases?

It becomes narrower and bimodal.

It becomes narrower and more normal.

It becomes wider and skewed right.

It becomes wider and more normal.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

28% of all Steele students believe Monday will be snow day. You take a sample of 50 students and find that 15 of them believe Monday will be a snow day. What is the probability of getting a sample of size 50 that has 15 (15/50 = 0.3) or more students who believe Monday will be a snow day?

0.376

Cannot be determined because the distribution of the sample proportion of samples of size 50 is not normal

0.624

0.99999

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The Gallup Poll asked a random sample of 100 adults whether they attended church during the past week. Let p-hat be the proportion of people in the sample who attended church. A newspaper report claims that 40% of all U.S. adults went to church last week. Suppose this claim is true.
Calculate the standard deviation of the sampling distribution.

0.002

0.049

0.04

0.001

MULTIPLE CHOICE QUESTION

1 min • 1 pt

28% of all Woodrow students believe Monday will be snow day. You take a sample of 50 students and find that 15 of them believe Monday will be a snow day. What does 50 represent?

phat

standard deviation

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What does this symbol represent?

population proportion

parameter

sample proportion

population sample

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Sampling Distributions

What happens to the shape of a sampling distribution of sample proportions as n increases?

28% of all Steele students believe Monday will be snow day. You take a sample of 50 students and find that 15 of them believe Monday will be a snow day. What is the probability of getting a sample of size 50 that has 15 (15/50 = 0.3) or more students who believe Monday will be a snow day?

28% of all Woodrow students believe Monday will be snow day. You take a sample of 50 students and find that 15 of them believe Monday will be a snow day. What does 50 represent?

What does this symbol represent?

What does this symbol represent?

What does this symbol represent?

10% of people are left handed. If 800 people are randomly selected, find the likelihood that at least 12% of the sample is left handed.

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