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 four decimal places.) (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.) (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.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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
(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.)
(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.)
(d) The home run percentages for three professional players are below.
| Player A, 2.5 | Player B, 2.1 | Player C, 3.8 |
Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.
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