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Homework01Chapter04

# Homework01Chapter04 - 190 CHAPTER 4 Statistical Sampling(d...

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190 CHAPTER 4 Statistical Sampling (d) K11allenge) The company's primary concern is to avoid underestimating the av- erage amount claimed by its policyholders. Determine a value b so that the in- surance company is 95% confident that the average amount claimed by its policyholders is b or less. EXERCISE 4.3 According to annual precipitation data kept for the past 75 years, the average precipitation in New York City is 41.76 inches per year and the ob- served sample standard deviation is 5.74 inches per year. (a) Construct a 99% confidence interval for the mean of the distribution of yearly precipitation in New York City. (b) Determine the required sample size in order to estimate the mean of the distrib- ution of yearly precipitation in New York City to within 1.2 inches at the 99% confidence level. (c) During the same 75-year period, the average precipitation in Tokyo was 34.37 inches per year and the observed sample standard deviation was 4.98 inches per year. Construct a 95% confidence interval for the difference between the mean yearly precipitation in New York and Tokyo. EXERCISE 4.4A company manufacturing stereo equipment claims that their personal CD player can be used for approximately 8 hours of continuous play when used with alkaline batteries. To provide this estimate, the company tested 35 CD players with new alkaline batteries and recorded the time at which the batteries in the players "lost power." The average time was 8.3hours with a sample standard deviation of 1.2hours. (a) Construct a 95% confidence interval for the mean time until a new alkaline bat- tery used in the CD player loses power. (b) Determine the required sample size in order to estimate the mean time until a new alkaline battery used in the CD player losespower to within :t 10minutes at the 99%confidence level. EXEROSE 4.5 A sporting equipment company manufactures IS-pound dumbbells. Toensure that the production line is functioning properly, 50 dumbbells were selected at random, and their weights were recorded. The observed sample mean weight of the 50 dumbbells was 16.87 lb. and the observed sample standard deviation was 1.44lb.

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Homework01Chapter04 - 190 CHAPTER 4 Statistical Sampling(d...

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