Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.5 inches. A baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 2.5 inches. The heights (in inches) of 20 randomly selected players are shown in the table. 72, 74, 71, 73, 76, 70, 77, 75, 72, 72, 77, 72, 75, 70, 73, 74, 75, 73, 74, 73 a. Calculate the value of the test statistic. b. Use technology to determine the P-value for the test statistic. c. What is the correct conclusion at the α=0.05 level of significance?
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.
Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.5 inches. A baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 2.5 inches. The heights (in inches) of 20 randomly selected players are shown in the table.
72, 74, 71, 73, 76, 70, 77, 75, 72, 72, 77, 72, 75, 70, 73, 74, 75, 73, 74, 73
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