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Statistics Exploring Study Set 1
Quiz 7: Survey Sampling and Inference
Path 4
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Question 41
Essay
Suppose that you and a friend read the following statement in a news report, "A recent pollfound 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'sa 95% chance that somewhere between 51% and 57% of voters plan to vote for candidateX!" How would you explain to your friend why his statement is incorrect, be sure toprovide your friend with the correct interpretation of the confidence interval.
Question 42
Short Answer
Use the following information to answer the question. An event planner does some research and finds that in the area wherea large children's event is to be held, approximately 1.75% of the children are lactose intolerant. Treat the 250 childrenexpected 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 belactose intolerant so he orders 7 lactose-free meals. What is the approximate probabilitythat 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.
Question 43
Essay
Can the way a survey question is asked affect the sample results? Explain why such asample is or is not reflective of the population.
Question 44
Short Answer
Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain25% "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? Howmany marbles would this be? Round to the nearest whole marble.
Question 45
Short Answer
Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain25% "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 %
--------------------
.
Question 46
Essay
Explain the difference between a population and a sample. Give an example of each.
Question 47
Essay
Frederick is interested in whether residents of his community are opposed to theconstruction of a party store on the corner of a busy intersection. He randomly polls 150residents in the community and receives responses from 55 residents. Of those whoresponded, 60% were opposed to the construction of the party store in the community soFrederick concludes that the majority of residents in his community oppose theconstruction of the party store. Explain what is wrong with this approach.
Question 48
Essay
Explain the difference between the standard error of a sample proportion and the marginof error of a confidence interval for a population proportion.
Question 49
Short Answer
Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain25% "milky-white" marbles. Suppose that a bag containing 80 marbles is inspected. -What is the margin of error, using a 95% confidence level, for estimating the trueproportion of adults who self-report that they cannot swim 24 yards? Round to the nearest thousandth.
Question 50
Essay
Suppose that Michigan lawmakers survey 500 randomly selected registered voters to see ifthey favor an extension of the fall duck hunting season. The lawmakers believe thepopulation proportion in favor of extending the duck hunting season is 45% (based onhistorical data and previous votes). State the three conditions of the Central Limit Theoremand explain whether each condition is satisfied in this scenario.
Question 51
Short Answer
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 lactoseintolerant, give or take how many? Round to the nearest whole person.
Question 52
Short Answer
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.
Question 53
Essay
Suppose a city manager conducts a poll and finds that a 95% confidence interval for theproportion of residents who support yard watering restrictions during extended periods ofno rain is 43% to 51%. Explain what the "95%" means.