3. Scenario It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver in nearly half of those tested. A researcher wants to conduct a study to estimate if the proportion of acetaminophen users who have liver damage is the same as previously reported. For participating in this study, he will pay each subject $20 and provide a free medical consultation if the patient has liver damage. Part A If he wants to limit the margin of error of his 98% confidence interval to 2%, what is the minimum number of subjects he needs? (answer should be in the form of x,xxx) the minimum amount of money he needs to set aside to pay his subjects? $ (answer should be in the form of $xx,xxx) Part B The amount you calculated in Part A is substantially over his budget so he decides to use fewer subjects. Will this change increase or decrease the width of his confidence interval? Will this new confidence interval be more precise or less precise?
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.
3. Scenario
It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver in nearly half of those tested. A researcher wants to conduct a study to estimate if the proportion of acetaminophen users who have liver damage is the same as previously reported. For participating in this study, he will pay each subject $20 and provide a free medical consultation if the patient has liver damage.
Part A
If he wants to limit the margin of error of his 98% confidence interval to 2%, what is
- the minimum number of subjects he needs? (answer should be in the form of x,xxx)
- the minimum amount of money he needs to set aside to pay his subjects? $ (answer should be in the form of $xx,xxx)
Part B
The amount you calculated in Part A is substantially over his budget so he decides to use fewer subjects.
- Will this change increase or decrease the width of his confidence interval?
- Will this new confidence interval be more precise or less precise?
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
