Chapter 9 Solutions - 203 Chapter 9 9.1(a =2.5003 is a parameter(related to the population of all the ball bearings in the container and x =2.5009 is a

Chapter 9 Solutions - 203 Chapter 9 9.1(a =2.5003 is a...

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Chapter 9 9.1 (a) µ =2.5003 is a parameter (related to the population of all the ball bearings in the container and x =2.5009 is a statistic (related to the sample of 100 ball bearings). (b) ˆ p =7.2% is a statistic (related to the sample of registered voters who were unemployed). 9.2 (a) ˆ p = 48% is a statistic; = 52% is a parameter. (b) Both p control x = 335 and experimental x = 289 are statistics. (c) Answers will vary. A histogram based on pooling the work of 25 students (250 simulated values of ˆp) is shown below (on the right). As expected, the simulated distribution of ˆpis approximately Normal with a center at 0.5. Simulated proportion Count of sample proportions 0.65 0.60 0.55 0.50 0.45 0.40 0.35 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Simulated proportion Count of sample proportions 0.750 0.675 0.600 0.525 0.450 0.375 0.300 60 50 40 30 20 10 0 (d) Answers will vary, but the standard deviation will be close to 0.5 0.5 0.1118 20 × ± . The simulation above for the pooled results for 25 students produced a standard deviation of 0.1072. (e) By combining the results from many students, he can get a more accurate estimate of the value of p since the value of ˆ p approaches p as the sample size increases. 203