Question 7.31 and 7.33 only
CHAPTER 7 STATISTICAL INFERENCE CONCERNING MEANS AND PROPORTIONS .28 Under laboratory test conditions a handball should bounce 48 inches. The manufacturer was receiving complaints that the balls were not as lively as they should be. The manufacturer ran- domly sampled 50 handballs and found a mean bounce of 46.5 inches and a standard deviation of 5 inches. At the 5% level of significance, is there sufficient evidence to suggest that the manufac turer's handballs are bouncing less than 48 inches on average? What type of error has possibly been committed? Explain the error in ordinary language. .29 To confirm her belief that abused children will show elevated levels of depression, a psychologist gave a test called the Profile of Mood States (POMS) to a sample of 50 abused children. The results showed a mean depression score of 17.3 and a standard deviation of 5.4. At the 5% level, can she conclude that abused children in general have a mean depression level of more than 15 (the mean for college students)? 30 Prior to expanding the facilities of a town library, it was determined that 385 books per day were loaned out. It was believed that a new addition to the building would increase the mean number of books loaned out per day. After completion of the new addition, a random sample of 35 days showed a mean of 395 and a standard deviation of 26 books loaned out per day. At the 10% level of significance, is there sufficient evidence to indicate that more books are being loaned out per day, on the average? .31 The owner of an artesian well-drilling company suspected that, for a large tract of development land, the average depth of water below the surface was less than 500 feet. A sample of 32 wells gave a mean depth of x = 486 feet and a standard deviation of s = 53 feet. At the 1% level of significance, is the owner's suspicion justified? 32 A plastic has a mean breaking strength of 27 and a standard deviation of 6 pounds per square inch. A new process is developed and will replace the old one, provided that there is substantial evidence that it improves the strength of the product. A random sample of 40 pieces made with the new process gives a sample mean of 30 pounds per square inch. (a) Assuming that the variability is unchanged (i.e., o = 6), is there sufficient evidence to suggest that the strength of the product has increased at the 1% level of significance? (b) Repeat part (a) using o = 15. Comment on the relationship between the ability to detect a change and the amount of spread of the data values about the mean. 33 A manufacturer of floor mops would like his product to last 700 hours, on the average. He hopes the mean number of hours is not a lot less than 700 (people will not continue to buy his product) or a lot more than 700 (people would seldom have to buy the product). However, the manufacturer has reason to believe the mean may have changed. A random sample of 48 items shows that x = 675 and s = 77 hours. (a) Complete the test at the 5% level of significance. (b) What type of error may have been made? (c) What is the probability of committing this error? 34 A cereal is packaged to contain 16 ounces, on the average. A consumer agency has received many complaints claiming that packages of the cereal contain less than 16 ounce- claim that the mean content u is less than To
