Compute the value of the test statistic. (Round your answer to 4 decimal places.) x² 13.5599
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.
Only the part in the red box (it is apart of part b)
![The color of the Star Trek uniform represents each
crew-member's work area. In the original Star Trek
series, blue shirts are worn by medical and science
staff, gold shirts are worn by the command division,
and the red shirts were worn by engineering,
security and communications division. We will
statistically assess whether there is a connection
between uniform color and the fatality rate. The
table below shows a sample of how many crew-
members in each area have died onscreen and their
shirt color. Use a =
0.05 to test to see if a crew-
member's fatality onscreen is dependent on their
uniform color.
Alive
Dead
Total
Blue
40
8
48
Gold
22
28
Red
29
27
56
Total
91
41
132
a. Choose the correct null and alternative
hypotheses.
Ho: There is no association between
Star Trek fatalities and uniform color.
H. There is an association between Star
а
Trek fatalities and uniform color.
Ho: There is an association between
Star Trek fatalities and uniform color.
H, There is no association between Star
а
Trek fatalities and uniform color.
b. Compute the test statistic.
Complete the following table of expected
counts. (Round your answers to 4 decimal
places).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe99d77bd-6783-440b-95ab-8e6a48270523%2F405d39fb-8cb4-40dd-974b-229bd6bf325c%2Fhs9v99s_processed.jpeg&w=3840&q=75)
![b. Compute the test statistic.
Complete the following table of expected
counts. (Round your answers to 4 decimal
places).
Alive
Dead
Blue
33.0909
14.9090
Gold
19.3030
8.6969
Red
38.6060
17.3939
Compute the value of the test statistic. (Round
your answer to 4 decimal places.)
13.5599
c. Compute the p-value. (Round your answer to 4
decimal places.)
p-value
0.0011
d. Interpret the results of the significance test.
O The p-value provides strong evidence
against the null hypothesis. The
association between Star Trek fatalities
and uniform color is statistically
significant.
The p-value provides little evidence
against the null hypothesis. The
association between Star Trek fatalities
and uniform color is not statistically
significant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe99d77bd-6783-440b-95ab-8e6a48270523%2F405d39fb-8cb4-40dd-974b-229bd6bf325c%2Fwdha97g_processed.jpeg&w=3840&q=75)
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