Find Probability of 3 Samples from Chi-Square Distribution Exceeding 7.779

In summary, the Chi-Square distribution is a statistical distribution used for analyzing categorical data. A value of 7.779 in this distribution represents a critical point, and exceeding it is considered statistically significant. Finding the probability of exceeding 7.779 for three samples means determining the likelihood of observing three independent events above this critical point. Calculating this probability is important as it helps determine the significance of the results. It can be calculated using a Chi-Square table or statistical software such as SPSS or R.
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Homework Statement



If 15 Observations are taken independently from a chi-square distribution with 4 degrees of freedom, find the probability that at most 3 of the 15 sample items exceed 7.779

Homework Equations


The Attempt at a Solution



This problem should be quite simple. I find that in the back of my text that the chi square distribution of 7.779 is .9... but the answer is .9444... I am at a loss at why it is not exactly .9 and where to go from here. I would appreciate any help. Thanks.
 
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Have you taken into consideration that the problem asks for "at most 3"?
 

What is the Chi-Square distribution?

The Chi-Square distribution is a statistical distribution that is commonly used to analyze categorical data. It is a continuous probability distribution that is characterized by a single parameter called the degrees of freedom.

What is the significance of exceeding 7.779 in the Chi-Square distribution?

In the Chi-Square distribution, the value of 7.779 represents a critical point or a cutoff point. It is the point at which the probability of obtaining a value greater than 7.779 is less than 5%. In other words, if the calculated Chi-Square value exceeds 7.779, it is considered statistically significant.

What does it mean to find the probability of 3 samples from the Chi-Square distribution exceeding 7.779?

This means that we are interested in finding the likelihood of obtaining a Chi-Square value greater than 7.779 for all three samples. In other words, we want to know the chance of observing three independent events that exceed the critical Chi-Square value of 7.779.

Why is it important to calculate the probability of exceeding 7.779 in the Chi-Square distribution?

Calculating the probability of exceeding 7.779 in the Chi-Square distribution allows us to determine the statistical significance of our results. If the calculated probability is less than 5%, it indicates that our results are unlikely to occur by chance and are therefore considered statistically significant.

How can I calculate the probability of 3 samples from the Chi-Square distribution exceeding 7.779?

The probability can be calculated by using the Chi-Square distribution table or using statistical software. First, calculate the Chi-Square value for each sample and then use the degrees of freedom and the Chi-Square table to find the corresponding probability. Alternatively, you can use statistical software such as SPSS or R to calculate the exact probability.

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