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Exam 20: Estimating Proportions With Confidence

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Question 21

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Explain (in words that a non-statistics student would understand) what is meant by a '95% confidence interval.'

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an interval of value...

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Question 22

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For Questions , use the following narrative Narrative: Bread machines Suppose a survey was done this year to find out what percentage of all Americans own a bread machine.Out of their random sample of 1,000 Americans, 317 own a bread machine.The margin of error for this survey was plus or minus 3%. -{Bread machine narrative} Suppose three years ago, 29% of Americans owned a bread machine.Based on the results of this current survey, what would you conclude (with high confidence) about the population of all Americans now compared with three years ago?

A) A larger proportion of Americans own a bread machine now compared to three years ago.
B) A smaller proportion of Americans own a bread machine now compared to three years ago.
C) The proportion of Americans who own a bread machine has not significantly changed from three years ago.
D) None of the above.

E) B) and D)
F) C) and D)

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Question 23

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A(n) _______________ is an interval of values computed from the sample data that is almost sure to cover the true population number.

A 95% confidence interval means that 95% of all possible random samples will result in an interval that contains the true population value, and 5% of them won't.How could a confidence interval that is based on a random sample not contain the true population value?

Statisticians have a phrase, "Being a statistician means never having to say you're certain." Do you know whether the confidence interval constructed by your sample actually contains the true population value? Why or why not?

What is the most common level of confidence used to construct confidence intervals?

Which of the following is a correct interpretation of a 90% confidence interval?

In which of the following situations can you construct a confidence interval for the population proportion with only what is given?

For Questions , use the following narrative Narrative: Bread machines Suppose a survey was done this year to find out what percentage of all Americans own a bread machine.Out of their random sample of 1,000 Americans, 317 own a bread machine.The margin of error for this survey was plus or minus 3%. -{Bread machine narrative} What proportion of the entire American population owns a bread machine, based on these results?

For Questions use the following narrative Narrative: Oranges Suppose a shipment of oranges is advertised to weigh 5 pounds per bag.We know that not every bag can contain exactly 5 pounds of oranges.We decide to take a random sample of 100 bags of oranges and find out what they tell us about the population of all bags in this shipment.We are only interested in whether or not the bags are underweight, so each bag is weighed and counted as underweight if it weighs less than 5 pounds.Five bags in our sample of 100 were found to be underweight. -{Oranges narrative} Suppose the grocery store who ordered the oranges will reject the shipment if they believe, based on these sample results, that more than 10% of the bags in the entire truckload are underweight.Based on our sample, will they have to return this shipment? Explain your answer.

Name two different situations that can result in a confidence interval for a proportion falling into negative numbers for some of its values (which does not make sense).Give an example of each.