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 2.6 inches. A baseball analyst wonders whether the standard deviation of heights of​ major-league baseball players is less than 2.6 inches. The heights​ (in inches) of 20 randomly selected players are shown in the table. LOADING... Click the icon to view the data table. Test the notion at the alpha equals 0.05α=0.05 level of significance. Data Table 72 74 71 73 76 70 77 76 72 72 77 72 75 70 73 74 75 73 74 74 What are the correct hypotheses for this​ test?   The null hypothesis is H0​: sigmaσ   equals=   2.6 The alternative hypothesis is H1​: sigmaσ   less than<   2.6 Calculate the value of the test statistic.   chi Subscript Superscript χ2 equals=??? ​(Round to three decimal places as​ needed.)

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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.