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Construction of 95 Percent Confidence Intervals

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In a sample of 500 new Web sites registered on the Internet, 24 were anonymous (i.e., they shielded their name and contact information). (a) Construct a 95 percent confidence interval for the proportion of all new Web sites that were anonymous.

A 2003 survey showed that 4.6 percent of the 250 Americans surveyed had suffered some kind of identity theft in the past 12 months. (a) Construct a 98 percent confidence interval for the true proportion of Americans who had suffered identify theft in the past 12 months. (b) May normality be assumed? Explain. (Data are from Scientific American 291, no. 6, p. 33.)

A special bumper was installed on selected vehicles in a large fleet. The dollar cost of body repairs was recorded for all vehicles that were involved in accidents over a 1-year period. Those with the special bumper are the test group and the other vehicles are the control group, shown below. Each "repair incident" is defined as an invoice (which might include more than one separate type of damage).
(a) Construct a 90 percent confidence interval for the true difference of the means assuming equal variances. Show all work clearly.

Construct a 95 percent confidence interval for the difference of mean monthly rent paid by undergraduates and graduate students. What do you conclude?

Exercise-Chapter 9
(Be sure and include the hypotheses and a written decision. Points will be taken off if a written decision is not included.)

Procyon Mfg. produces tennis balls. Weights are supposed to be normally distributed with a mean of 2.035 ounces and a standard deviation of 0.002 ounces. A sample of 25 tennis balls shows a mean weight of 2.036 ounces. At α = .025 in a right-tailed test, is the mean weight heavier than it is supposed to be?

The mean arrival rate of flights at O'Hare Airport in marginal weather is 195 flights per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days of marginal weather the mean arrival rate is 200 flights per hour. (a) Set up a right-tailed decision rule at α=.025 to decide whether there has been a significant increase in the mean number of arrivals per hour. (b) Carry out the test and make the decision. Is it close? Would the decision be different if you used α = .01? (c) What assumptions are you making, if any?

An airline serves bottles of Galena Spring Water that are supposed to contain an average of 10 ounces. The filling process follows a normal distribution with process standard deviation 0.07 ounce. Twelve randomly chosen bottles had the weights shown below (in ounces). (a) Set up a two-tailed decision rule to detect quality control violations using the 5 percent level of significance. (b) Carry out the test. (c) What assumptions are you making, if any?

The manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour. (a) At α = .05 in a left-tailed test, would a sample of 16 randomly chosen hours with a mean of 510 and a standard deviation of 50 indicate that the manufacturer's claim is overstated? (b) Why might the assumption of a normal population be doubtful? (See Aviation Week and Space Technology 162, no. 4 (January 24, 2005), p. 42.)

The manufacturer of Glo-More flatwhite interior latex paint claims one-coat coverage of 400 square feet per gallon on interior walls. A painter keeps careful track of 6 gallons and finds coverage (in square feet) of 360, 410, 380, 360, 390, 400. (a) At α = .10 does this evidence contradict the claim?

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Solution Summary

The solution construction a 95 percent confidence intervals for different statistical scenarios are given.