Describe as specifically possible the following for this study: as Population Sample Observational Unit
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![Vitamin E and the Risk of Prostate Cancer: Klien et al (2011) conducted the
following study to determine the effect of vitamin E and selenium treatment on
the risk of developing prostate cancer in healthy men. A total of 34,887 men
from different study sites in the United States, Canada, and Puerto Rico were
randomly selected. To be eligible to participate, the men had to take a rectal
examination that showed he was not suspicious of having prostate cancer and
be aged 50 years or older for black men and 55 years or older for all others.
Each man was randomly assigned to receive one of four treatments: selenium,
vitamin E, selenium and vitamin E together, or a placebo. The men were
followed up after 8 years to see if they had developed prostate cancer or not.
The main question of interest is to determine if the risk of developing prostate
cancer differs by the treatment taken. The data are summarized in the table
below:
No Prostate Cancer Prostate Cancer
Total
Selenium
8,752
8,737
8,702
8,696
34,887
8177
575
Vitamin E
8117
620
Selenium and Vitamin E
8147
555
Placebo
8167
529
Total
32,608
2,279](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e3700f1-4cb8-4852-a5cd-588e0eb7c40a%2Fdb4e7048-9d6b-459f-8687-1a1c759dad32%2F28n8ooe_processed.png&w=3840&q=75)
![Describe as specifically as possible the following for this study:
• Population
• Sample
• Observational Unit
• Experimental Unit
• Variables - Specify which are quantitative and which are categorical and further
classify each as Nominal, Ordinal, Interval, or Ratio. Specify which are explanatory
and which are response variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e3700f1-4cb8-4852-a5cd-588e0eb7c40a%2Fdb4e7048-9d6b-459f-8687-1a1c759dad32%2Fujow1km_processed.png&w=3840&q=75)
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