The National Center for Health Statistics reports that the average systolic blood pressure for males 35-44 years of age has a mean of 122. The medical director of a large company believes the average systolic blood pressure for male executives 35-44 years of age at his company is different from 122. He looks at the medical records of 64 randomly selected male executives in this age group and finds that the mean systolic blood pressure in this sample is 125.5 and the standard deviation is 24. The sample does not contain any outliers. Suppose you want to create a confidence interval for μ, the true average systolic blood pressure of all 35-44-year-old male executives at this company. Are all assumptions met to create this confidence interval? No, none of the assumptions are met. It is impossible to determine. We know one assumption is met. We are unsure about the second assumption, but since the method is robust, it is okay. The confidence interval is still valid.
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.
The National Center for Health Statistics reports that the average systolic blood pressure for males 35-44 years of age has a mean of 122. The medical director of a large company believes the average systolic blood pressure for male executives 35-44 years of age at his company is different from 122. He looks at the medical records of 64 randomly selected male executives in this age group and finds that the mean systolic blood pressure in this sample is 125.5 and the standard deviation is 24. The sample does not contain any outliers. Suppose you want to create a confidence interval for μ, the true average systolic blood pressure of all 35-44-year-old male executives at this company. Are all assumptions met to create this confidence interval?
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