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a. What value of chi-square for 5 degrees of freedom subdivides the area under the distribution curve such that \(5 \%\) is to the right and \(95 \%\) is to the left? b. What is the value of the 95 th percentile for the chi-square distribution with 5 degrees of freedom? c. What is the value of the 90th percentile for the chi-square distribution with 5 degrees of freedom?

In the past the standard deviation of weights of certain 32.0 -oz packages filled by a machine was 0.25 oz. A random sample of 20 packages showed a standard deviation of 0.35 oz. Is the apparent increase in variability significant at the 0.10 level of significance? Assume package weight is normally distributed. a. Solve using the \(p\) -value approach. b. Solve using the classical approach.

A manufacturer of television sets claims that the maintenance expenditures for its product will average no more than \(110\)dollar during the first year following the expiration of the warranty. A consumer group has asked you to substantiate or discredit the claim. The results of a random sample of 50 owners of such television sets showed that the mean expenditure was \(131.60\)dollar and the standard deviation was \(42.46\)dollar At the 0.01 level of significance, should you conclude that the manufacturer's claim is true or not likely to be true?

Today's newspapers and magazines often report the findings of survey polls about various aspects of life. The Pew Internet \& American Life Project (January 13-February 9,2005 ) found that "63\% of cell phone users ages \(18-27\) have used text messaging within the past month." Other information obtained from the project included "random telephone survey of 1,460 cell phone users" and "has a margin of sampling error of plus or minus 3 percentage points." Relate this information to the statistical inferences you have been studying in this chapter. a. Is a percentage of people a population parameter, and if so, how is it related to any of the parameters that we have studied? b. Based on the information given, find the \(95 \%\) confidence interval for the true proportion of cell phone users who have used text messaging. c. Explain how the terms "point estimate," "level of confidence," "maximum error of estimate," and "confidence interval" relate to the values reported in the article and to your answers in part b.