Question 1

Explain the difference between a statistic and a parameter. Give an example of each.

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Question 2

Suppose that you and a friend read the following statement in a news report, "A recent poll found that 54% of voters, give or take 3%, plan to vote for candidate X in the next election (with a confidence level of 95%)." Your friend then makes the statement, "Hey, look, there's a 95% chance that somewhere between 51% and 57% of voters plan to vote for candidate X!" How would you explain to your friend why his statement is incorrect, be sure to provide your friend with the correct interpretation of the confidence interval.

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Question 3

A survey of 800 randomly selected senior citizens showed that 55% said they planned to watch an upcoming political debate on television. The margin of error for the 95% confidence interval is 3.5 percentage points. Does the confidence interval support the claim that the majority of senior citizens plan to watch the upcoming political debate on television? Explain why or why not.

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Question 4

Explain the difference between the standard error of a sample proportion and the margin of error of a confidence interval for a population proportion.

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Question 5

Use the following information to answer the question. In a recent poll of 900 randomly selected adults, 37% reported that they could not swim 24 yards (the length of a typical gymnasium lap pool).
-What is the standard error for the estimate of the proportion of all adults that self- report that they cannot swim 24 yards? Round to the nearest ten- thousandth.

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Question 6

Use the following information to answer the question. In a recent poll of 900 randomly selected adults, 37% reported that they could not swim 24 yards (the length of a typical gymnasium lap pool).
-What is the margin of error, using a 95% confidence level, for estimating the true proportion of adults who self- report that they cannot swim 24 yards? Round to the nearest thousandth.

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Question 7

A polling agency wants to determine the size of the random sample needed to estimate the proportion of voters who favor proposal X. The estimate should have a margin of error no more than 4.5 percentage points at a 95% level of confidence. Determine the minimum size of the sample, rounding to the nearest whole person.

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Question 8

A sampling method should be as precise and accurate as possible. Explain what these two terms mean and how each is measured.

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Question 9

Suppose that Michigan lawmakers survey 500 randomly selected registered voters to see if they favor an extension of the fall duck hunting season. The lawmakers believe the population proportion in favor of extending the duck hunting season is 45% (based on historical data and previous votes). State the three conditions of the Central Limit Theorem and explain whether each condition is satisfied in this scenario.

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Question 10

Use the following information to answer the question. An event planner does some research and finds that in the area where a large children's event is to be held, approximately 1.75% of the children are lactose intolerant. Treat the 250 children expected at the event as a simple random sample from the local population of about 100,000 children.
-Suppose the event planner assumes that only 0.8% of the children attending the event will be lactose intolerant so he orders 2 lactose- free meals. What is the approximate probability that he will have too many lactose- free meals? Round to the nearest thousandth.

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Question 11

Use the following information to answer the question. In a recent poll of 900 randomly selected adults, 37% reported that they could not swim 24 yards (the length of a typical gymnasium lap pool).
-Report the 95% confidence interval for the proportion of adults who self- report that they cannot swim 24 yards. Round final calculations to the nearest tenth of a percent.

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Question 12

Can the way a survey question is asked affect the sample results? Explain why such a sample is or is not reflective of the population.

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Question 13

Use the following information to answer the question. An event planner does some research and finds that in the area where a large children's event is to be held, approximately 1.75% of the children are lactose intolerant. Treat the 250 children expected at the event as a simple random sample from the local population of about 100,000 children.
-On average, how many of the children attending the event would be expected to be lactose intolerant, give or take how many? Round to the nearest whole person.

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Question 14

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain 25% "milky- white" marbles. Suppose that a bag containing 80 marbles is inspected.
-What value should we expect for our sampling percentage of milky- white marbles? How many marbles would this be? Round to the nearest whole marble.

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Question 15

Use the following information to answer the question. An event planner does some research and finds that in the area where a large children's event is to be held, approximately 1.75% of the children are lactose intolerant. Treat the 250 children expected at the event as a simple random sample from the local population of about 100,000 children.
-Suppose the event planner assumes that 2.8% of the children attending the event will be lactose intolerant so he orders 7 lactose- free meals. What is the approximate probability that more than 2.8% of the children attending the event are lactose intolerant and that he will not have enough lactose- free meals? Round to the nearest thousandth.

Accepted Answer

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Question 16

Suppose a city manager conducts a poll and finds that a 95% confidence interval for the proportion of residents who support yard watering restrictions during extended periods of no rain is 43% to 51%. Explain what the "95%" means.

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Question 17

Explain the difference between a population and a sample. Give an example of each.

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Question 18

Frederick is interested in whether residents of his community are opposed to the construction of a party store on the corner of a busy intersection. He randomly polls 150 residents in the community and receives responses from 55 residents. Of those who responded, 60% were opposed to the construction of the party store in the community so Frederick concludes that the majority of residents in his community oppose the construction of the party store. Explain what is wrong with this approach.

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Question 19

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain 25% "milky- white" marbles. Suppose that a bag containing 80 marbles is inspected.
-What is the standard error? Round to the nearest tenth of a percent.

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Question 20

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain 25% "milky- white" marbles. Suppose that a bag containing 80 marbles is inspected.
-Use your answers to fill in the blanks: We expect % milky- white marbles, give or take %.

Accepted Answer

The answer of Use the following information to answer the...

Quiz 7: Survey Sampling and Inference

Explain the difference between a statistic and a parameter. Give an example of each.

Explain the difference between the standard error of a sample proportion and the margin of error of a confidence interval for a population proportion.

A sampling method should be as precise and accurate as possible. Explain what these two terms mean and how each is measured.

Can the way a survey question is asked affect the sample results? Explain why such a sample is or is not reflective of the population.

Suppose a city manager conducts a poll and finds that a 95% confidence interval for the proportion of residents who support yard watering restrictions during extended periods of no rain is 43% to 51%. Explain what the "95%" means.

Explain the difference between a population and a sample. Give an example of each.

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain 25% "milky- white" marbles. Suppose that a bag containing 80 marbles is inspected. -What is the standard error? Round to the nearest tenth of a percent.

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain 25% "milky- white" marbles. Suppose that a bag containing 80 marbles is inspected. -Use your answers to fill in the blanks: We expect % milky- white marbles, give or take %.