I want to flip this button for confidence interval, and I want to make sure that the level matches what's asked for in the problem, which is 99%. The sample size we're given here in the problem. So now I can put that number here in this field in my options window. So if I take out my calculator here, I put in that sample standard deviation, and I square it. If we remember that variance is simply the standard deviation squared, I can get the sample variance I need by squaring the sample standard deviation. Well, we're not given variance here, but we are given sample standard deviation. Here in the options window, I'm asked to calculate the sample variance. To do that, I'm going to come back here to StatCrunch, and I'm going to go to Stat -> Variance Stats (because that's how we calculate anything with standard deviation inside the StatCrunch application) -> One Sample (because I have only one sample) -> With Summary (because I don't have actual data). Fantastic!Īnd now the last part asks for a confidence interval estimate on the population standard deviation. And I'm asked around to three decimal places. The one on the left (which is the subscript L) is the one we want first. So I put 99% in, I press Compute, and here we've got our two critical values. So what we need to put in here is the area in between the critical values, and that's the size of the confidence level, which in this case is 99%. Here in these spaces are where our critical values are going to show up. Degrees of freedom are what we calculated in the first part. There are two that we're looking for, and so I'm going to have to use the Between option. So I know I need the Chi-squared distribution. I know I need the chi-squared calculator because, if I look here at the statistic I'm being asked to calculate, this is chi-squared. So to access the distribution calculator, I need to go to Stat -> Calculators -> Chi-squared. Let's pop that window out, and let's resize it so we can get a better look at what's going on here. To get the critical values out, I'm going to load up StatCrunch and access the distribution calculator that is to be found inside StatCrunch. The one on the left is what's being asked for here. You may notice that the F-test of an overall significance is a particular form of the F-test for comparing two nested models: it tests whether our model does significantly better than the model with no predictors (i.e., the intercept-only model).Now the next part asks us for the first of two critical values. The test statistic follows the F-distribution with (k 2 - k 1, n - k 2)-degrees of freedom, where k 1 and k 2 are the numbers of variables in the smaller and bigger models, respectively, and n is the sample size. You can do it by hand or use our coefficient of determination calculator.Ī test to compare two nested regression models. With the presence of the linear relationship having been established in your data sample with the above test, you can calculate the coefficient of determination, R 2, which indicates the strength of this relationship. The test statistic has an F-distribution with (k - 1, n - k)-degrees of freedom, where n is the sample size, and k is the number of variables (including the intercept). We arrive at the F-distribution with (k - 1, n - k)-degrees of freedom, where k is the number of groups, and n is the total sample size (in all groups together).Ī test for overall significance of regression analysis. Its test statistic follows the F-distribution with (n - 1, m - 1)-degrees of freedom, where n and m are the respective sample sizes.ĪNOVA is used to test the equality of means in three or more groups that come from normally distributed populations with equal variances. All of them are right-tailed tests.Ī test for the equality of variances in two normally distributed populations. P-value = 2 × min, we denote the smaller of the numbers a and b.)īelow we list the most important tests that produce F-scores. Right-tailed test: p-value = Pr(S ≥ x | H 0) Left-tailed test: p-value = Pr(S ≤ x | H 0) In the formulas below, S stands for a test statistic, x for the value it produced for a given sample, and Pr(event | H 0) is the probability of an event, calculated under the assumption that H 0 is true: It is the alternative hypothesis that determines what "extreme" actually means, so the p-value depends on the alternative hypothesis that you state: left-tailed, right-tailed, or two-tailed. More intuitively, p-value answers the question:Īssuming that I live in a world where the null hypothesis holds, how probable is it that, for another sample, the test I'm performing will generate a value at least as extreme as the one I observed for the sample I already have? It is crucial to remember that this probability is calculated under the assumption that the null hypothesis H 0 is true! Formally, the p-value is the probability that the test statistic will produce values at least as extreme as the value it produced for your sample.
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