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.Construct a confidence interval of the population

1).Construct a confidence interval of the population

proportion at the given level of confidence?

x equals

x=860

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860​, n equals

n=1100

1100​, 99

99​% confidence

2).A poll of 1125

1125 adults in a certain country found that 55

55​% identified themselves as the followers of some religion. The margin of error was 5

5 percentage points with 90

90​% confidence.

Which of the following represents a reasonable interpretation of the survey​ results?

A.

There is 90

90​% confidence that the proportion of adults in a certain country who identify themselves as the followers of some religion is between 50

50​% and 60

60​%.

B.

There is between 85

85​% and 95

95​% confidence that 55

55​% of adults in a certain country identify themselves as the followers of some religion.

C.

There is 90

90​% confidence that 55

55​% of adults in a certain country identify themselves as the followers of some religion.

D.

In 90

90​% of samples of adults in a certain​ country, the proportion who identify themselves as the followers of some religion is between 50

50​% and 60

60​%.

3). In a trial of 400

400 patients who received​ 10-mg doses of a drug​ daily, 48

48 reported headache as a side effect. Use this information to complete parts​ (a) through​ (d) below.

4).A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03

0.03 with 90

90​% confidence if

​(a) she uses a previous estimate of 0.42

0.42​?

​(b) she does not use any prior​ estimates?

5).Katrina wants to estimate the proportion of adults who read at least 10 books last year. To do​ so, she obtains a simple random sample of 100 adults and constructs a​95% confidence interval. Matthew also wants to estimate the proportion of adults who read at least 10 books last year. He obtains a simple random sample of 400 adults and constructs a​ 99% confidence interval. Assuming both Katrina and Matthew obtained the same point​ estimate, whose estimate will have the smaller margin of​error? Justify your answer.

Whose estimate will have the smaller margin of error and​ why?

A.

​Katrina’s estimate will have the smaller margin of error because the lower level of confidence more than compensates for the smaller sample size.

B.

​Katrina’s estimate will have the smaller margin of error because the sample size is smaller and the level of confidence is lower.

C.

​Matthew’s estimate will have the smaller margin of error because the larger sample size more than compensates for the higher level of confidence.

D.

​Matthew’s estimate will have the smaller margin of error because the sample size is larger and the level of confidence is higher.

6).In a​ survey, 1400

1400 adults in a certain country were asked how many hours they worked in the previous week. Based on the​ results, a​ 95% confidence interval for mean number of hours worked was lower​ bound: 38.4

38.4 and upper​ bound: 41.1

41.1. Which of the following represents a reasonable interpretation of the​ result? For those that are not​ reasonable, explain the flaw.

​(a) There is a​ 95% chance the mean number of hours worked by adults in this country in the previous week was between 38.4

38.4 hours and 41.1

41.1 hours.

A.

Flawed. This interpretation makes an implication about individuals rather than the mean.

B.

Flawed. This interpretation implies that the population mean varies rather than the interval.

C.

Flawed. This interpretation implies that the mean is only for last week.

D.

Correct

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 931

931 people age 15 or​ older, the mean amount of time spent eating or drinking per day is 1.15

1.15 hours with a standard deviation of 0.74

0.74 hour.

​(a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.

A.

The distribution of the sample mean will never be approximately normal.

B.

Since the distribution of time spent eating and drinking each day is not normally distributed​ (skewed right), the sample must be large so that the distribution of the sample mean will be approximately normal.

C.

Since the distribution of time spent eating and drinking each day is normally​ distributed, the sample must be large so that the distribution of the sample mean will be approximately normal.

D.

The distribution of the sample mean will always be approximately normal.

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