6 Questions
What is the probability of obtaining a sample variance S^2 between 3.462 and 10.745 from a random sample of 25 observations?
0.95
What type of distribution is used to calculate the probability of obtaining a sample variance within a certain range?
Chi-square distribution
How does the population variance affect the calculation of the probability for the sample variance?
It directly affects the chi-square distribution used to calculate the probability.
What is the probability of obtaining a sample variance S^2 between 3.462 and 10.745 from a random sample of 25 observations?
0.95
How does the size of the random sample affect the probability of obtaining a sample variance within a certain range?
The probability decreases as the sample size increases.
What is the impact of the population variance on the probability of obtaining a sample variance within a certain range?
A larger population variance leads to a higher probability of obtaining extreme sample variances.
Calculate the probability of obtaining a sample variance between 3.462 and 10.745 from a random sample of 25 observations, drawn from a normal population with variance σ^2 = 6. This involves applying the chi-square distribution to find the probability.
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