Review Exercises

Subject: Introduction to Statistics

  1. The percentage of Americans 25 years or older who have at least some college education is 50.9%. In a random sample of 300 Americans 25 years old and older, what is the probability that more than 175 have at least some college education?
  1. Two out of five adult smokers acquired the habit by age 14. If 400 smokers are randomly selected, find the probability that 170 or more acquired the habit by age 14.
  1. The average cholesterol content of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.
  1. If a single egg is selected, find the probability that the cholesterol content will be greater 220 milligrams.
  2. If a sample of 25 eggs is selected, find the probability that the mean of the sample will be larger than 220 milligrams
  1. The sugar content (in grams for a random sample of 4-ounce containers of applesauce is shown. Find the 99% confidence interval for the population variance and standard deviation. Assume the variable is normally distributed.

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5.The number of calories in a 1-ounce serving of various kinds of regular cheese is shown. Estimate the population variance and standard deviation with 90% confidence.

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6.A service station advertises that customers will have to wait no more than 30 minutes for an oil change. A sample of 28 oil changes has a standard deviation 5.2 minutes. Find the 95% confidence interval of the population standard deviation of the spent waiting for an oil change.

7.A health care professional wishes to estimate the birth weights of infants. How large a sample must she select if she desires to be 90% confident that the true mean is within 6 ounces of the sample mean? The standard deviation of the birth weights is known to be 8 ounces.

8.A random sample of the number of barrels (in millions) of oil produced per day by world oil-producing countries is listed here. Estimate the mean oil production with 95% confidence.

9.The number of grams of carbohydrates in a 12 ounce serving of a regular soft drink is listed here for a random sample of sodas. Estimate the mean number of carbohydrates in all brands of soda with 95% confidence.

10.The proportion of students in private schools is around 11 percent. A random sample of 450 students from a wide geographic area indicated that 55 attended private schools. Estimate the true proportion of students attending private schools with 95% confidence.

11.A survey found that out of 200 workers, 168 said they were interrupted three or more times an hour by phone messages, faxes, etc. Find the 90% confidence interval of the population proportion of workers who are interrupted three or more times an hour.

12.Last year the average cost of making a movie was $54.8 million. This year, a random sample of 15 recent action movies had an average production cost of $62.3 million with a variance of $90.25 million. At the 0.05 level of significance, can it be concluded that it costs more than average to produce an action movie?

13.A car dealer recommends that transmissions be serviced at 30,000 miles. To see whether her customers are adhering to this recommendation, the dealer selects a sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the sample is $1684. By finding the P-value, determine whether the owners are having their transmissions serviced at 30,000 miles. Use

  1. A telephone company wants to advertise that more than 30% of all its customers have more than two telephones. To support this ad, the company selects a sample of 200 customers and finds that 72 have more than two telephones. Does the evidence support the ad? Use. Use the P-value method.
  1. The average hourly wage last year for members of the hospital clerical staff in a large city was $6.32. The standard deviation of the population was $0.54. This year a sample of 50 workers had an average hourly wage of $6.51. Test the claim, at, that the average has not has not changed by finding the P-value for the test.
  1. A random sample of 20 different kinds of doughnuts had the following calorie contents. At , is there enough evidence to conclude that the standard deviation is greater than 20 calories?

19.A nutritionist claims that the standard deviation of the number of calories in one tablespoon of the major brands of pancake syrup is 60. A sample of major brands of syrup is selected, and the number of calories is shown. At, can the claim be rejected?

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