Test the following claim. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Tests of older baseballs showed that when dropped 22 ft onto a concrete surface, they bounced an average of 236.82 cm. In a test of 40 new baseballs, the bounce heights had a mean of 231.3 cm. Assume that the standard deviation of bounce heights of all new baseballs is 4.24 cm. Use a 0.05 significance level to test the claim that the new baseballs have bounce heights with a mean different from 236.8 cm. Are the new baseballs different? What is the value of the test statistic? Identify the critical value(s) of z.
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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