Compute a 99% confidence interval (in percentages) for the population mean μ of 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 %
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.
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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= x bar = %
s = %
(b)
Compute a 90% confidence interval (in percentages) for the population mean μ 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. (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 mean μ of 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 %
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