Question
1. The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave
1. 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 findands(in percentages). (For each answer, enter a number. Round your answers to two decimal places.)
x bar = % s= % (b) Compute a 90% confidence interval (in percentages) for the population meanof home run percentages for all professional baseball players.Hint:If you use theStudent'stdistribution table, be sure to use the closestd.f.that issmaller. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit % (c) Compute a 99% confidence interval (in percentages) for the population meanof home run percentages for all professional baseball players. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit % (d) The home run percentages for three professional players are below.
Player A,2.5 | Player B,2.4 | Player C,3.8 |
Examine your confidence intervals and describe how the home run percentages for these players compare to the population average. i. We can say Player A falls close to the average, Player B is above average, and Player C is below average.
ii. We can say Player A falls close to the average, Player B is below average, and Player C is above average.
iii. We can say Player A and Player B fall close to the average, while Player C is above average.
iv. We can say Player A and Player B fall close to the average, while Player C is below average.
2. What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (For each answer, enter a number. Round your answers up the nearest whole number.)
(a)a preliminary estimate for p is 0.22 (b)there is no preliminary estimate for p
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