Question Completion Status: QUESTION & Suppose a team of clinical psychologists develops a test to predict which patients who are treated with opioid painkillers develop a serious problem called Opioid Use Disorder (OUD). Let's suppose that the tests are right 80% of the time both in predicting which patients treated with an opioid will develop Opioid Use Disorder and which will not. That's a pretty good test. Suppose we give the tes to 1,000 people with the partial results shown here. In that case, here is the question: ACTUAL OUD Not OUD Predict OUD 80 TEST RESULT Predict Not OUD 720 100 900 1,000 What is the likelihood (percent of the time) that a person who is predicted to develop OUD actually does so (that is, he or she actually develops the OUD)? 80 / 720 = 11% 720 /900 = 80% 80 / 260 = 31% 260 / 1,000 = 26%
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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