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Intro to Stat_Part_54

# Intro to Stat_Part_54 - 176 CHAPTER 11 THE CHI-SQUARE...

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176 CHAPTER 11. THE CHI-SQUARE DISTRIBUTION Exercise 11.19 (Solution on p. 183.) Isabella, an accomplished Bay to Breakers runner, claims that the standard deviation for her time to run the 7 ½ mile race is at most 3 minutes. To test her claim, Rupinder looks up 5 of her race times. They are 55 minutes, 61 minutes, 58 minutes, 63 minutes, and 57 minutes. Exercise 11.20 Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. They are also interested in the variation of the number of babies. Suppose that an airline executive believes the average number of babies on flights is 6 with a variance of 9 at most. The airline conducts a survey. The results of the 18 flights surveyed give a sample average of 6.4 with a sample standard deviation of 3.9. Conduct a hypothesis test of the airline executive’s belief. Exercise 11.21 (Solution on p. 183.) According to the U.S. Bureau of the Census, United Nations, in 1994 the number of births per woman in China was 1.8. This fertility rate has been attributed to the law passed in 1979 restricting births to one per woman. Suppose that a group of students studied whether or not the standard deviation of births per woman was greater than 0.75. They asked 50 women across China the number of births they had. Below are the results. Does the students’ survey indicate that the standard deviation is greater than 0.75? # of births Frequency 0 5 1 30 2 10 3 5 Table 11.16 Exercise 11.22 According to an avid aquariest, the average number of fish in a 20–gallon tank is 10, with a standard deviation of 2. His friend, also an aquariest, does not believe that the standard deviation is 2. She counts the number of fish in 15 other 20–gallon tanks. Based on the results that follow, do you think that the standard deviation is different from 2? Data: 11; 10; 9; 10; 10; 11; 11; 10; 12; 9; 7; 9; 11; 10; 11 Exercise 11.23 (Solution on p. 183.)

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