## Ander.dlearn.kmu.edu.tw

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*• *Please choose any 100 points from all 130 points to answer.

It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amountof time is actually a normally distributed random variable whose mean is 7.5 days and whosestandard deviation is 1.2 days.

(a) What proportion of cold sufferers experiences less than 4 days of symptoms?
(b) What proportion of cold sufferers experiences symptoms between 7 and 10 days.

A psychologist believe that 80% of male drivers when lost continue to drive, hoping to findthe location they seek rather than ask directions. To examine this belief, he took a randomsample of 350 male drivers and asked each what they did when lost. If the belief is true,determine the probability that less than 75% said they continue driving.

The average North American loses an average of 15 days per year due to colds and flu. Thenatural remedy echinacea is reputed to boost the immune system. One manufacturer ofechinacea pills claims that consumers of its product will reduce the number of days lost tocolds and flu by one-third. To test the claim, a random sample of 50 people was drawn.

Half took echinacea, and the other half took placebos. If we assume that the standard devi-ation of the number of days lost to colds and flu with and without echinacea is 3 days, findthe probability that the mean number of days lost for echinacea users is less than that fornonusers.

One of the few negative side effects of quitting smoking is weight gain. Suppose that theweight gain in the 12 months following a cessation in smoking is normally distributed witha standard deviation of 6 pounds. To estimate the mean weight gain, a random sampleof 15 quitters was drawn and their weights recorded and listed here. Determine the 90%confidence interval estimate of the mean 12-month-weight gain for all quitters.

A medical researcher wants to investigate the amount of time it takes for patients’ headachepain to be relieved after taking a new prescription painkiller. She plans to use statisticalmethods to estimate the mean of the population of relief times. She believe that the popu-lation is normally distributed with a standard deviation of 15 minutes. How large a sampleshould she take to estimate the mean time to within 1 minute with 99% confidence?
A dean of a business school claims that the GMAT scores of applications to the school’sM.B.A. program have increased during the past 5 years. Five years ago, the mean andstandard deviation of GMAT scores of M.B.A. applications were 560 and 50, respectively.

Twenty applications for this year’s program were randomly selected and the GMAT scoresrecorded. If we assume that the distribution of GMAT scores of this year’s applicants is thesame as that of 5 years ago, with the possible exception of the mean, can we conclude at the5% significance level that the dean’s claim is true?
A school-board administrator believes that the average number of days absent per yearamong students is less than 10 days. From past experience, he knows that the populationstandard deviation is 3 days. In testing to determine whether his believe is true, he coulduse one of the following plans:
i.

*n *= 100

*, α *=

*.*01
Which plan has the lowest probability of a Type II error, given that the true populationaverage is 9 days?
Home blood-pressure monitors have been on the market for several years. This device allowspeople with high blood pressure to measure their own and determine whether additionalmedication is necessary. Concern has been expressed about inaccurate readings. To judgethe severity of the problem, a laboratory technician measured his own blood pressure 25times using the leading brand of monitors. Estimate the population variance with 95%confidence.

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In some states the law requires drivers to turn on their headlights when driving in the rain.

A highway patrol officer believes that less than one-quarter of all drivers follow this rule.

As a test, he randomly samples 150 cars driving in the rain and counts the number whoseheadlights are turned on. He finds this number to be 31. Does the officer have enoughevidence at the 10% significance level to support his belief?
In segmenting the breakfast cereal market, a food manufacturer uses health and diet con-sciousness as the segmentation variable. Four segments are developed:
1. Concerned about eating healthy foods2. Concerned primarily about weight3. Concerned about health because of illness4. Unconcerned
To distinguish between groups, surveys are conducted. On the basis of a questionnaire,people are categorized as belonging to one of these groups. A recent survey asked a randomsample of 1,250 American adults (20 and over) to complete the questionnaire. The categorieswere recorded using the codes. The most recent census reveals that there are 207,347,000Americans who are 20 and over. Estimate with 95% confidence the number of Americanadults who are concerned about eating healthy foods.

Source: http://ander.dlearn.kmu.edu.tw/fall06/Statistics/final_f06.pdf

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