An author has written 5 children’s books. The numbers of pages in these books are 64, 66, 71, 73, and 76. List all 10 possible SRSs of size n = 3. Is the sample median a biased or unbiased estimator of the population median? Explain

mean of sample medians ≠ population median

mean of sample medians = population median

An author has written 5 children’s books. The numbers of pages in these books are 64, 66, 71, 73, and 76. Describe how the variability of the sampling distribution of the sample median would change if the sample size was increased to n = 4.

as sample size, n , increases → sample standard deviation, $$\sigma_{\overline{x}}$$ , decreases

as sample size, n , increases → data increases in variability

A report claimed that 20% of respondents subscribe to the “5-second rule” That is, they would eat a piece of food that fell onto the kitchen floor if it was picked up within 5 seconds. Assume this figure is true for the population of U.S. adults. Let p ̂ = the proportion of people who subscribe to the 5-second rule in an SRS of size 80 from this population. Interpret the standard deviation you found.

In SRSs of n = 80, sample proportion of people who follow 5-sec rule typically varies from true population by 0.045 sec

In SRSs of n = 80, sample proportion of people who follow 5-sec rule typically varies from true population by 0.20 sec

people who follow 5-sec rule typically vary from true population by 0.045 sec

In SRSs of n = 80, sample proportion of people who follow 5-sec rule is typically 0.20 sec

A report claimed that 20% of respondents subscribe to the “5-second rule” That is, they would eat a piece of food that fell onto the kitchen floor if it was picked up within 5 seconds. Assume this figure is true for the population of U.S. adults. Let p ̂ = the proportion of people who subscribe to the 5-second rule in an SRS of size 80 from this population. Justify whether it is appropriate to use a normal distribution to model the sampling distribution of p ̂.

There is not enough information

A report claimed that 20% of respondents subscribe to the “5-second rule” That is, they would eat a piece of food that fell onto the kitchen floor if it was picked up within 5 seconds. Assume this figure is true for the population of U.S. adults. Let p ̂ = the proportion of people who subscribe to the 5-second rule in an SRS of size 80 from this population. In an actual SRS of size 80, only 10% subscribed to the 5-second rule. Based on your answer to the previous problem, is there convincing evidence that the proportion of all U.S. adults who subscribe to the 5-second rule is less than 0.20? Explain.

That could not happen by chance alone

The probability was less than 5%

That could happen by chance alone

Commercially raised Copper Rockfish have lengths that are approximately normally distributed with a mean of 16.4 inches and a standard deviation of 2.1 inches. Let $$\overline{x}$$ = the mean length in a random sample of 10 commercially raised Copper Rockfish. Interpret the standard deviation you found.

In SRSs of n = 10, sample mean length of rockfish varies from true mean by about 0.664 inches

In SRSs of n = 10, sample mean length of rockfish varies from true mean by about 16.4 inches

sample mean length of rockfish varies from true mean by about 0.664 inches

In SRSs of n = 10, sample mean length of rockfish is about 16.4 inches

Commercially raised Copper Rockfish have lengths that are approximately normally distributed with a mean of 16.4 inches and a standard deviation of 2.1 inches. Let $$\overline{x}$$ = the mean length in a random sample of 10 commercially raised Copper Rockfish. Which answers to the previous problems would be affected if the distribution of length in the population of commercially raised Copper Rockfish was distinctly non-normal. Explain.

Cannot use the standard normal z-table

None, they all still use the same formulas

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, and SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distributions of moth counts is strongly skewed with mean 0.5 and standard deviation 0.7. In a recent month, the mean number of moths in an SRS of size 50 was 0.6. Based on this result, should the state agricultural department be worried that the moth population is getting larger in their state? Explain your reasoning.

That could happen by chance alone

That could not happen by chance alone

The probability was less than 5%

Stats: Review Chapter 11 - Sampling Distributions

Authored by Diana Boehmer

Mathematics

12th Grade

CCSS covered

Stats: Review Chapter 11 - Sampling Distributions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

People who eat eggs that are contaminated with salmonella can get food poisoning. A large egg producer randomly selects 200 eggs from all the eggs shipped in one day. The laboratory reports that 9/200 = 0.045 of these eggs had salmonella contamination. Identify the POPULATION, the parameter, the sample, and the statistic.

200 eggs that are randomly selected per day

all eggs shipped in one day

proportion of eggs shipped that are contaminated with salmonella

proportion, 0.045, of eggs sampled that are contaminated with salmonella

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

People who eat eggs that are contaminated with salmonella can get food poisoning. A large egg producer randomly selects 200 eggs from all the eggs shipped in one day. The laboratory reports that 9/200 = 0.045 of these eggs had salmonella contamination. Identify the population, the PARAMETER, the sample, and the statistic.

200 eggs that are randomly selected per day

all eggs shipped in one day

proportion of eggs shipped that are contaminated with salmonella

proportion, 0.045, of eggs sampled that are contaminated with salmonella

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

People who eat eggs that are contaminated with salmonella can get food poisoning. A large egg producer randomly selects 200 eggs from all the eggs shipped in one day. The laboratory reports that 9/200 = 0.045 of these eggs had salmonella contamination. Identify the population, the parameter, the SAMPLE, and the statistic.

200 eggs that are randomly selected per day

all eggs shipped in one day

proportion of eggs shipped that are contaminated with salmonella

proportion, 0.045, of eggs sampled that are contaminated with salmonella

Tags

CCSS.HSS.IC.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

People who eat eggs that are contaminated with salmonella can get food poisoning. A large egg producer randomly selects 200 eggs from all the eggs shipped in one day. The laboratory reports that 9/200 = 0.045 of these eggs had salmonella contamination. Identify the population, the parameter, the sample, and the STATISTIC.

200 eggs that are randomly selected per day

all eggs shipped in one day

proportion of eggs shipped that are contaminated with salmonella

proportion, 0.045, of eggs sampled that are contaminated with salmonella

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

An author has written 5 children’s books. The numbers of pages in these books are 64, 66, 71, 73, and 76. List all 10 possible SRSs of size n = 3. Which of the following is not a possible SRS?

{64, 66, 76}

{66, 71, 73}

{64, 71, 73, 76}

{76, 66, 71}

Tags

CCSS.7.SP.A.2

MULTIPLE SELECT QUESTION

15 mins • 1 pt

An author has written 5 children’s books. The numbers of pages in these books are 64, 66, 71, 73, and 76. List all 10 possible SRSs of size n = 3. Calculate the median number of pages for each sample and display the sampling distribution of the sample median on a dot plot. What are the possible medians for the SRSs?

74.5

FILL IN THE BLANK QUESTION

15 mins • 1 pt

An author has written 5 children’s books. The numbers of pages in these books are 64, 66, 71, 73, and 76. List all 10 possible SRSs of size n = 3. Calculate the median number of pages for each sample and display the sampling distribution of the sample median on a dot plot. How many dots above 66 on the number line for the dot plot?

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Stats: Review Chapter 11 - Sampling Distributions

An author has written 5 children’s books. The numbers of pages in these books are 64, 66, 71, 73, and 76. List all 10 possible SRSs of size n = 3. Which of the following is not a possible SRS?

An author has written 5 children’s books. The numbers of pages in these books are 64, 66, 71, 73, and 76. List all 10 possible SRSs of size n = 3. Provided the dot plot of the sampling distribution of the sample median, calculate the mean of the sample medians.

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