A researcher wishes to test the effectiveness of a new flu vaccination. There are 150 people who are vaccinated with Vaccine A, 180 are vaccinated with Vaccine B and 100 people are not vaccinated. Independent simple random samples were used and the number in each group who later caught the flu was recorded. Table 2 shows the test group and the flu status. Table 2: Status for Vaccine A, Vaccine B and No Vaccine Vaccine A Vaccine B No Vaccine Got flu 13 25 21 No flu 137 155 79 At the 0.1 level of significance, is the new flu vaccination effective? Conduct the chi-square test to support your justification.
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.
![A researcher wishes to test the effectiveness of a new flu vaccination. There are 150 people
who are vaccinated with Vaccine A, 180 are vaccinated with Vaccine B and 100 people are not
vaccinated. Independent simple random samples were used and the number in each group
who later caught the flu was recorded. Table 2 shows the test group and the flu status.
Table 2: Status for Vaccine A, Vaccine B and No Vaccine
Vaccine A
Vaccine B
No Vaccine
Got flu
13
25
21
No flu
137
155
79
At the 0.1 level of significance, is the new flu vaccination effective? Conduct the chi-square
test to support your justification.
Given the hypothesis statement as:
Họ:There is no effect of the new flu vaccine to the test groups.
Hi:There is a significant effect of the new flu vaccine to the test groups.
Calculate the x² test value:
The expected value is given as below:
Vaccine A
Vaccine B
No Vaccine
Observed
Expected
20.6
Observed
Expected
Observed
Expected
Caught the flu
Did not catch the flu
13
25
24.7
21
13.7
137
129.4
155
155.3
79
86.3
Fill in the blank cells:
Cell value (oj, eij) [Oij -eij)]?/ eij
(13, 20.6)
(137, 129.4)
(25, 24.7)
(155, 155.3)
0.001
(21, 13.7)
(79, 86.3)
Thus, the x?test
Get the critical value (x?cv):
Critical value (x²cv)=x²
State the conclusion of your test:
We
• the null hypothesis; there is evidence that the new vaccine is
• to fight the flu.
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