Name:_________________________



Name:_________________________

Date:__________Period:_________

Confidence Interval Take home TEST

Part 1: Multiple Choice. (2 points each)

Hand write the letter corresponding to the best answer in space provided on page 6.

_____1. A survey was conducted to determine what percentage of college seniors would have chosen to attend a different college if they had known then what they know now. In a random sample of 100 seniors, 34 percent indicated that they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who would have attended a different college

a) 24.7% to 43.3%

b) 25.8% to 42.2%

c) 26.2% to 41.8%

d) 30.6% to 37.4%

e) 31.2% to 36.8%

_____2. A 95 percent confidence interval of the form [pic] will be used to obtain an estimate for an unknown population proportion p. If [pic] is the sample proportion and E is the margin of error, which of the following is the smallest sample size that will guarantee a margin of error of at most 0.08?

a) 25

b) 100

c) 175

d) 250

e) 625

_____11. You want to compute a 96% confidence interval for a population mean. Assume that the population standard deviation is known to be 10 and the sample size 50. The value of z* to be used in this calculation is

a) 1.960

b) 1.645

c) 1.7507

d) 2.0537

e) None of the Above.

_____12. You want to estimate the mean SAT score for a population of students with 90% confidence interval. Assume that the population standard deviation is [pic]=100. If you want the margin of error to be approximately 10, you will need a sample size of

a) 16

b) 271

c) 38

d) 1476

e) None of the Above.

_____5. A 90 percent confidence interval is to be created to estimate the proportion of television viewers in a certain area who favor moving the broadcast of the late weeknight news to an hour earlier than it is currently. Initially, the confidence interval will be created using a simple random sample of 9,000 viewers in the area. Assuming that the sample proportion does not change, what would be the relationship between the width of the original confidence interval and the width of a second 90 percent confidence interval that is created based on a sample of only 1,000 viewers in the area?

a) The second confidence interval would be 9 times as wide as the original confidence interval.

b) The second confidence interval would be 3 times as wide as the original confidence interval.

c) The width of the second confidence interval would be equal to the width of the original confidence interval.

d) The second confidence interval would be [pic] times as wide as the original confidence interval.

e) The second confidence interval would be [pic] times as wide as the original confidence interval.

_____6. You have measured the systolic blood pressure of a random sample of 25 employees of a company located in Livingston. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138). Which of the following statements gives a valid interpretation of this interval?

a) Ninety-five percent of the sample of employees has a systolic blood pressure between 122 and 138.

b) Ninety-five percent of the population of employees has a systolic blood pressure between 122 and 138.

c) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

d) The probability that the population mean blood systolic blood pressure is between 122 and 138 is .95.

e) If the procedure were repeated many times, 95% of the sample means would be between 122 and 138.

f) None of the Above.

_____7. A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think that the drinking age should be lowered to eighteen. To find this out he poses the following question to his listeners. “Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?” He asks listeners to phone in and vote “yes” if they agree that the drinking age should be lowered and “no” if not. Of the 100 people who phoned in 70 answered “yes”. Which of the following conditions for inference about proportion using a confidence interval are violated?

a) The data are an SRS for the population of interest.

b) The population is at least ten times as large as the sample.

c) n is so large that both the count of successes np and count of failures n(1-p) are ten or more.

d) There appear to be no violations.

e) More than one condition is violated.

_____8. In preparing to use a t procedure, suppose we were not sure if the population was normal. In which of the following circumstances would we not be safe using a t procedure?

a) A stemplot of the data is roughly bell shaped.

b) A histogram of the data shows moderate skewness.

c) A stemplot of the data has a large outlier.

d) The sample standard deviation is large.

e) The t procedures are robust, so it is always safe.

_____9. The diameter of ball bearings is known to be normally distributed with unknown mean and variance. A random sample of size 25 gave a mean 2.5 cm. The 95% confidence interval had length 4 cm. Then

a) The sample variance is 4.86.

b) The sample variance is 26.03.

c) The population variance is 4.84.

d) The population variance is 23.56.

e) The sample variance is 23.56.

_____10. You want to compute a 90% confidence interval for the mean population with unknown population standard deviation. The sample size is 30. The value of t* you would use for this interval is

a) 1.96

b) 1.645

c) 1.699

d) .90

e) None of the Above

_____11. A 95% confidence interval for the mean reading achievement score for a population of third-grade students is (44.2, 54.2). The margin of error of this interval is

a) 95%

b) 5

c) 2.5

d) 10

e) The answer cannot be determined from the information given.

_____12. Which of the following is an example of a matched pairs design?

a) A teacher compares the pre-test and post-test scores of students.

b) A teacher compares the scores of students using a computer based method of instruction with the scores of other students using traditional method of instruction.

c) A teacher compares the scores of students in her class on a standardized test with the national average.

d) A teacher calculates the average of scores of students on a pair of tests and wishes to see if this average is larger than 80%.

e) None of these.

_____13. The effect of acid rain upon the yield of crops is of concern in many places. In order to determine baseline yields, a sample of 13 fields was selected, and the yield of barley (g/400m2) was determined. The output from SAS (this is a statistical program that summarizes data) appears below:

| | | | | | |QUANTILES (DEF=4) | | | |EXTREMES |

|N |13 |SUM WGTS |13 |100% |MAX |392 |99% |392 |LOW |HIGH |

|MEAN |220.231 |SUM |2863 |75% |Q3 |234 |95% |392 |161 |225 |

|STD DEV |58.5721 |VAR |3430.69 |50% |MED |221 |90% |330 |168 |232 |

|SKEW |2.21591 |KURT |6.61979 |25% |Q1 |174 |10% |163 |169 |236 |

|USS |671689 |CSS |41168.3 |0% |MIN |161 |5% |161 |179 |239 |

|CV |26.5958 |STD MEAN |16.245 | | | |1% |161 |205 |392 |

A 95% confidence interval for the mean yield is:

a) 220.2 [pic] 1.96(58.6)

b) 220.2 [pic] 1.96(16.2)

c) 220.2 [pic] 2.18(58.6)

d) 220.2 [pic] 2.18(16.2)

e) 220.2 [pic] 2.16(16.2)

_____14. An analysis, using a random sample of n = 500 families, obtained a 90% confidence interval for mean monthly family income for a large population: ($600, $800). If the analyst had used 99% confidence coefficient instead, the confidence interval would be:

a) Narrower and would involve a larger risk of being incorrect

b) Wider and would involve a smaller risk of being incorrect

c) Narrower and would involve a smaller risk of being incorrect

d) Wider and would involve a larger risk of being incorrect

e) Wider but it cannot be determined whether the risk of being incorrect would be larger or smaller

_____15. A 95% confidence interval for p, the proportion of Canadian root beer drinkers who prefer A&W was found to be (0.0236, 0.282). Suppose that the same poll was repeated in the United States (whose population is 10 times larger than Canada), but in this new poll, four times the number of people were interviewed. The resulting 95% confidence intervals will be:

a) About 1/2 as wide as the Canadian interval

b) About 1/4 as wide as the Canadian interval

c) About 1/10 as wide as the Canadian interval

d) About 4/10 as wide as the Canadian interval

e) The same size as the Canadian interval

_____16. A magazine has 1,620,000 subscribers, of whom 640,000 are women and 980,000 are men. Thirty percent of the women read the advertisements in the magazine and 50 percent of the men read the advertisements in the magazine. A random sample of 100 subscribers is selected. What is the expected number of subscribers in the sample who read the advertisements?

a) 30

b) 40

c) 42

d) 50

e) 80

_____17. The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is closest to

a) 60

b) 62

c) 68

d) 70

e) 74

_____18. The student government at a high school wants to conduct a survey of student opinion. It wants to begin with a simple random sample of 60 students. Which of the following survey methods will produce a simple random sample?

a) Survey the first 60 students to arrive at school in the morning.

b) Survey every 10th student entering the school library until 60 students are surveyed.

c) Use random numbers to choose 15 each of first-year, second-year, third-year, and fourth-year students.

d) Number the cafeteria seats. Use a table of random numbers to choose seats and interview the students until 60 have been interviewed.

e) Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey

_____19. There is a linear relationship between the number of chirps made by the striped ground cricket and air temperature. A least squares fit of some data collected by a biologist gives the model

[pic] 9 < x < 25,

Where x is the number of chirps per minute and [pic] is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?

a) 3.3o F

b) 16.5 o F

c) 25.2 o F

d) 28.5 o F

e) 41.7 o F

_____20. A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to determine which of two MP3 players just developed by a new company was preferred. To which of the following populations can the results of this survey be safely generalized?

a) Only people aged nineteen to thirty living in the state of Colorado who were in this survey

b) Only people aged nineteen to thirty living in the state of Colorado

c) All people living in the State of Colorado

d) Only people aged nineteen to thirty living in the United States

e) All people living in the United States

Name:___________________________

Date:_____________Period:________

PART I answers

|1. |2. |3. |4. |5. |

|6. |7. |8. |9 |10. |

|11. |12. |13. |14. |15. |

|16. |17. |18. |19. |20. |

PART II - Answer completely, but be concise. Write sequentially and show all steps. Show all your work. Indicate clearly the methods you used, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanations.

YOU MUST WRITE ANSWERS IN BY HAND – you need not print out the first 6 pages.

21. At Livingston High School a popular achievement test is used for college placement. Counselors selected a random sample of 100 students from Livingston High School and scored their tests by hand before sending them in for computer processing. For this sample,[pic]. Construct a 99% confidence interval for [pic], the population mean score for Livingston High.

(2,6,4,4 pts)

22.One difficulty in measuring the nesting success of birds is that the researchers must count the eggs in the nest, which is disturbing to the parents. Even though the researcher does not harm the birds, the flight of the bird might alert predators to the presence of a nest. To see if researcher activity might degrade nesting success, the nest survival of 102 nests that had their eggs counted, was recorded. Sixty-four of the nests failed (i.e. the parent abandoned the nest.)

a) Construct and interpret a 95% confidence interval for the proportion of nest failures in the population. (2,6,4,4 pts)

b) The "normal" nest failure rate of these birds is 29%. Based on the confidence interval from part (a), do you think that the researcher's activity affects nesting success? Justify your answer with an appropriate statistical argument. (4 points)

23. Local health authorities are concerned that the hectic pace in their city has elevated the stress, and thus the blood pressure of women. The authorities have decided to study this issue by measuring the blood pressure of a random sample of patients in the city over the next year and estimating the mean blood pressure, [pic], of women in the city. Blood pressure is approximately normally distributed in humans, and a 15-year-old study suggests the standard deviation of women's blood pressure is about 8 mm Hg. Suppose the health authorities accept this value as a reasonable estimate of the standard deviation of blood pressure of today's women in this city. If it is desired to estimate [pic] to within 1.0 mm Hg with 95% confidence, what sample size is necessary? (4 points)

24. When the hatching of young geese is very near, the father guards the nest to defend it from predators that may be attracted by the hatchlings noisy entrance into the world. The following data are the typical distances from the nest for 24 soon to be father geese. A biologist would like to construct a 95% confidence interval for the mean distance of future father geese from the nest during this period. (Distances are km.) (8 points – 4 each)

|2.0 |4.5 |5.6 |5.7 |5.8 |4.9 |

|4.4 |4.7 |5.9 |5.6 |5.3 |5.4 |

|6.3 |5.0 |5.5 |5.6 |5.5 |5.2 |

|5.6 |5.4 |4.9 |5.4 |5.3 |4.5 |

a) Using a graphical display of your choice, display the data in a way that will allow you to determine whether it would be appropriate to use a 95% t confidence interval to estimate the population mean.

b) Using the graphical display from part (a), would you advise that constructing a 95% confidence interval is appropriate? Provide statistical justification for your answer.

25. The Blue Shell Shuttle Bus Company has recently acquired the rights to run a shuttle between Lonestar’s hotels and its airport, which is several miles away. For the new route, the company has a choice of running coaches that can carry up to 60 people or smaller cans that can carry up to 12 people. The company has a policy that each of its routes is served only by one type of shuttle vehicle. In addition, due to the allocation of their vehicles to other routes, no change in their decision can be considered for at least a year. The annual return (profit or loss) depends on whether the demand for the service is strong or weak. Research suggests that the following returns can be expected. (16 points)

| |Annual Return ($10,000) | |

| |Demand | |

|Vehicle Decision |Strong |Weak |

|Coach |84 |-27 |

|Van |61 |45 |

For instance, if a coach is used and demand is strong, the expected annual return is $840,000. The expected return to the company can be calculated based on the probability ofa strong demand. Let p represent the probability of strong demand: then (1 – p) represents the probability of weak demand.

An equation that can be used to compute the expected return from the use of coaches based on the value of p is

84p + (-27)(1 – p) = 111p – 27.

An equation that can be used to compute the expected return from the use of vans based on the value of p is

61p + 45(1 – p) = 16p + 45.

These two functions are shown on the graph:

[pic]

a) The value of p for which the expected annual return for the vans is equal to the expected annual return for the coaches is 0.76. If the probability of strong demand is less than this value, which decision, running coaches of running vans, will provide the greater expected return? Justify your answer.

b) There are several thousand markets similar to Lonestar’s market across the country. A random sample of 100 of these markets reveals that the demand for an airport shuttle is strong in 65 of them and the demand in the remaining 35 weeks is weak. Using the results of this sample, construct and interpret a 95 percent confidence interval for the proportion of similar markets that will experience a strong demand.

c) The president of Blue Shell had decided to use vans for the new route. Using the results of the analysis in parts (a) and (b), write a few sentences to justify this decision.

d) After looking at the interval in part (b) and considering possible annual returns, the vice president of Blue Shell believes that the president has made an incorrect decision in choosing to use vans. Explain how this conflicting position could be supported

I pledge that the answers to the questions on this test have been formulated by myself and that I can explain and reproduce all the answers on my own if asked:_______________________________

105 points total/100

______

100 .

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