Question

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages. 1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4 (a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = 2.29 Correct: Your answer is correct. % s = 1.40 Correct: Your answer is correct. % (b) Compute a 90% confidence interval for the population mean ? of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.) lower limit % upper limit % (c) Compute a 99% confidence interval for the population mean ? of home run percentages for all professional baseball players. (Round your answers to two decimal places.) lower limit % upper limit %

Answer 1

• We will first calculate the mean and standard deviation
• The mean is given by
• =98.6/43=2.29
• The standard deviation is given by =1.40
• To calculate the 90% confidence interval is given by
• The critical value at =0.05 at 42 degrees of freedom of t distribution is given by 1.682.
• 0.90=P(-1.682<t(0,05,42)<1.682)
• 0.90=P(-1.682<<1.682)
• now substituting the calculated values the confidence interval obtained is
• (1.93<<2.649)
• To calculate the 99% confidence interval
• The critical value at =0.005 at 42 degrees of freedom of t distribution is given by 2.698
• 0.99=P(-2.698<t(0.005,42)<2.698)
• 0.99=P(-2.698<<2.698)
• now substituting the calculated values the confidence interval obtained is
• (1.714<<2.866)