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Chapter 8: Q.2.2 (page 490)

Alcohol abuse has been described by college presidents as the number one problem on campus, and it is an important cause of death in young adults. How common is it? A survey of 10,904 randomly selected U.S. college students collected information on drinking behavior and alcohol-related problems.9 The researchers defined 鈥渇requent binge drinking鈥� as having five or more drinks in row three or more times in the past two weeks. According to this definition, 2486 students were classified as frequent binge drinkers

Check conditions for constructing a confidence interval for the parameter

Short Answer

Expert verified

The following conditions are satisfied below

a. Students were randomly chosen.

b. Number of failures and successes are at least10.

Step by step solution

01

Step       1 Given Information

Given that,

Number of students (n)=10904

Number of binger drivers (x)=2486

Confidence level=99%

02

Explanation

The following are the main conditions for the population proportion confidence interval:

  1. The information must be random.
  2. Values must be unrelated to one another.
  3. The number of successes and failures should be greater than or equal to ten.
  4. The sample size should not exceed 10% of the population.

The following requirements are met below

  1. Students were picked at random.
  2. There are at least 10 failures and achievements.
  3. Students were chosen at random.

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Most popular questions from this chapter

Price cuts (4.2) Stores advertise price reductions to attract customers. What type of price cut is most attractive? Experiments with more than one factor allow insight into interactions between the factors. A study of the attractiveness of advertised price discounts had two factors: percent of all foods on sale (25%,50%,75%,or100%)and whether the discount was stated precisely (as in, for example, 鈥�60%off鈥�) or as a range (as in 鈥�40%to 70%off鈥�). Subjects rated the attractiveness of the sale on a scale of 1 to 7. (a) Describe a completely randomized design using 200student subjects. (b) Explain how you would use the partial table of random digits below to assign subjects to treatment groups. Then use your method to select the first 3subjects for one of the treatment groups. Show your work clearly on your paper.

(c) The figure below shows the mean ratings for the eight treatments formed from the two factors. Based on these results, write a careful description of how percent on sale and precise discount versus range of discounts influence the attractiveness of a sale.

63. Give it some gas! Computers in some vehicles calculate various quantities related to performance. One of these is fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle
equipped in this way, the miles per gallon were recorded each time the gas tank was filled and the computer was then reset. Here are the mpg values for a random sample of 20of these records:

15.813.615.619.122.415.622.517.219.422.6
19.418.014.618.721.014.822.621.514.320.9
Construct and interpret a 95% confidence interval for the mean fuel efficiency M for this vehicle.

Engine parts Here are measurements (in millimeters) of a critical dimension on an SRS of 16of the more than 200auto engine crankshafts produced in one day:

224.120, 224.001, 224.017,223.982,223.989,223.960,224.089,223.987,223.976,223.902,223.980,224.098,224.057,223.913,223.999

(a) Construct and interpret a 95%confidence interval for the process mean at the time these crankshafts were produced.

(b) The process mean is supposed to be 渭=224but can drift away from this target during production. Does your interval from part (a) suggest that the process mean has drifted? Explain.

- Determine the sample size required to obtain a level Cconfidence interval for a population mean with a specified margin of error.

A 90% confidence interval for the mean M of a population is computed from a random sample and is found to be 9 卤3. Which of the following could be the 95% confidence interval based on the same data?

(a) 9 卤1.96 (b) 9 卤2 (c) 9 卤3 (d) 9 卤4

(e) Without knowing the sample size, any of the above answers could be the 95% confidence interval.

Power lines and cancer (4.2,4.3)Does living near power lines cause leukemia in children? The

National Cancer Institute spent 5 years and $5million gathering data on this question. The researchers compared 638children who had leukemia with620who did not. They went into the homes and actually measured the magnetic fields in children's bedrooms, in other rooms, and at the front door. They recorded facts about power lines near the family home and also near the mother's residence when she was pregnant. Result: no connection between leukemia and exposure to magnetic fields of the kind produced by power lines was found.

(a) Was this an observational study or an experiment? Justify your answer.

(b) Does this study show that living near power lines doesn't cause cancer? Explain.
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