Data show that men between the ages of 20 and 29 have a mean height of 69.3 inches, with a standard deviation of 2.6 inches. A baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less t 2.6 inches. The heights (in inches) of 20 randomly selected players are shown in the table. Complete parts (a) through (c) below. E Click the icon to view the data table. (a) Are the given data normally distributed? (Check by constructing a normal probability plot.) O A. No, the normal probability plot has a curve. O B. No, not all the data lie within the bounds of the normal probability plot. Data Table OC. No, the plot has a curve and some of the data do not lie within the bounds. O D. Yes, the data come from a distribution that is approximately normal. (b) Compute the sample standard deviation. 72 74 71 71 76 74 72 77 72 75 70 73 74 75 73 74 74 s= inches 70 77 (Round to two decimal places as needed.) (c) Test the notion at the a =0.10 level of significance. What are the correct hypotheses for this test? Print Done The null hypothesis is Ho: 2.6. The alternative hypothesis is H,: ▼2.6. Calculate the value of the test statistic. xổ = (Round to two decimal places as needed.) Use technology to determine the P-value for the test statistic. The P-value is

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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.