1. The length of stay in a hospital after receiving a particular treatment is of interest to the patient, the hospital, and insurance providers. Of particular interest are unusually short or long lengths of stay. A random sample of 50 patients who received the treatment was selected, and the length of stay, in number of days, was recorded for each patient. The results are summarized in the following table and are shown in the dotplot. Length of stay (days) 5 4 13 7 8 12 21 Number of patients 14 11 1 1
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.
(b) Consider two rules for identifying outliers, method A and method B. Let method A represent the
1.5 ¥ IQR rule, and let method B represent the 2 standard deviations rule.
(i) Using method A, determine any data points that are potential outliers in the distribution of length of
stay. Justify your answer.
(ii) The
(c) Explain why method A might identify more data points as potential outliers than method B for a distribution that is strongly skewed to the right.
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Researchers will conduct a year-long investigation of walking and cholesterol levels in adults. They will
select a random sample of 100 adults from the target population to participate as subjects in the study.
(a) One aspect of the study is to record the number of miles each subject walks per day. The researchers are deciding whether to have subjects wear an activity tracker to record the data or to have subjects keep a daily journal of the miles they walk each day. Describe what bias could be introduced by keeping the daily journal instead of wearing the activity tracker.
During the course of the study, the subjects will have their cholesterol levels measured each month by a doctor. The researchers will perform a significance test at the end of the study to determine whether the average cholesterol level for subjects who walk fewer miles each day is greater than for those who walk more miles each day.
(b) Selecting a random sample creates a reasonable representative sample of the target population. Explain the benefit of using a representative sample from the population.
(c) Suppose the researchers conduct the test and find a statistically significant result. Would it be valid to claim that increased walking causes a decrease in average cholesterol levels for adults in the target population? Explain your reasoning.
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