Preventable chronic diseases are increasing rapidly in Native American populations particularly diabetes. Following is a contingency table showing cross classification of educational attainment and diabetic state for a sample of 500 Native Americans (HS is High School). Do these data provide sufficient evidence at the 5% significance level to infer that there are differences in education among the diabetic state? Diabetic State Education Level Less than HS HS Grad College Grad Total Type 1 110 124 1 235 Type 2 67 85 1 153 No diabetic 37 72 3 112 Total 214 281 5 500
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.
Preventable chronic diseases are increasing rapidly in Native American populations particularly diabetes.
Following is a
for a sample of 500 Native Americans (HS is High School). Do these data provide sufficient evidence at
the 5% significance level to infer that there are differences in education among the diabetic state?
Diabetic
State
Education Level
Less than HS HS Grad College
Grad Total
Type 1 110 124 1 235
Type 2 67 85 1 153
No diabetic 37 72 3 112
Total 214 281 5 500
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