In Exercises 27–30, find the critical values and for the level...

Question

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.95, n = 13

Accepted Answer

Hi all, and welcome back. The next problem says, for a confidence level of C equals 0.98, and a sample size of N equals 21. Find the critical values for chi squared on the right and on the left. And we have 4 answer choices, which just are different values for these 2. So, choice A, the right-sided critical value of chi squared 40.289. D, left-sided value 8.260. Choice B, the right-sided value 37.566. The left-sided value, 11.591. Choice C, the right-sided value 37.566. The left-sided value being 8.260. And choice D, right-sided value 40.289, and left-sided value, 11.591. So we're going to be looking up our values on a chi squared table where we'll need alpha. So we'll use our critical value to find alpha. So we know that alpha will equal. 1 minus the critical value, so 1 minus 0.98. So it's going to equal 0.02. However, since we have a two-sided test, we know that the area. In either tail. is equal to alpha divided by 2, so that will equal 0.01. So that's what we're going to use as our alpha, essentially, in looking at the table values. And then we also need our degrees of freedom. Which would be N minus 1, or N is 21, so that will equal 20. So, those are the two numbers we need to look up our on our chi squared table. But because we're looking for right and left values, our chi squared tables are usually given to us, and then the textbooks given in a right-sided form. So, we'll start with our right-sided critical value, since that will be the more straightforward one. So we use that 0.01 as our alpha, 20 as our degrees of freedom. And when we look that up on the table, that will give us a value of 37. 566. Now, on the left side, recall, we're looking for the probability that the value falls on the right side of this critical value. So, that's going to be this high probability, leaving us just this tail on the left of 0.01. So to get that right sided probability. We need to subtract 1 minus 0.01. And that will equal 0.99. So we'll use that as the alpha value. For the left sided Value. So using 0.99 and then 20 degrees of freedom. We get our left-sided critical value from the table as 8.260. And comparing those to answer choices, we see that these two numbers match choice C. All of our other answer choices involve incorrect cells on that table finding the number incorrectly. So, again, if we have a confidence level of 0.98, sample size of 21, the critical values on the right and the left for chi squared are choice C. Our right-sided critical value is 37.566. And our left-sided critical value is 8.260. See you in the next video.

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.
c = 0.95, n = 13

Key Concepts

Critical Values

Level of Confidence (c)

Sample Size (n)

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