More variation means there's more room for error to creep in, and you're going to be producing more defective products. The new production method is worse than the old one because you have more variation. So the variation appears to be greater than in the past, so the new method appears to be worse. So if we have sufficient evidence to support the claim that our standard deviation is now greater than what it was before, that means we have more variation in our process than we did before. 32.2, as we learned from the problem statement, is the standard deviation for the old production method. That means we're supporting the claim that our standard deviation is greater than 32.2. Nice work!Īnd now, the final part of the problem asks us to translate the results of the hypothesis test into real-world terms. Notice there's only one critical value because I have a one-tailed test, a right tailed test. I press Compute!, and here is my critical value, which is this value here bounding the critical region. So here in this probability field, I'm going to put 0.05. Here in the problem statement, we see we are instructed to use a 5% level of significance. My inequality sign needs to match my alternative hypothesis, which was “greater than.”Īnd then here in the probability field, I need to insert the significance level that I'm using to test, because the area for the critical region is the significance level for your hypothesis test. I want to find the critical value, so I need to clear out this default value in this field. I have 12 values in my sample data set, so this is going to be 11. My degrees of freedom is 1 less than my sample size. I'm using the chi-square calculator because this is the distribution for hypothesis testing on standard deviations. So I go to Stat –> Calculator –> Chi-square.
To do that, I'm going to pull up the chi-square calculator. The next part of our problem asks us to find the critical values.
It's the second to last value here in the table, and I put that in my answer field. For hypothesis testing, that is not necessary. Now I'm all ready to hit Compute!, and here's my answer option.Įarlier when doing confidence intervals, you need to take the square root of the upper and lower limits that come out of the results window here. And now I make sure that the inequality sign for my alternative hypotheses match. So I take out my calculator, 32.2 squared is 1036.84. So we need to take this value of 32.2 and square it to put here into the null hypothesis field.
But remember that because we're testing on variance, this is sigma squared, and our hypotheses have just sigma. In the hypothesis test area, I'm going to make sure these fields match the hypotheses that I selected from the previous part of the problem. I select the column where my data is located. Now that my data set is here in StatCrunch, I’m going to go into Stat –> Variance Stats (because this is the only option StatCrunch has for testing standard deviations and hypothesis testing) –> One Sample (because I have only one sample) –> With Data (because I have an actual data set). I'm going to select this icon right here and open my data set that's given to me in StatCrunch. Now we're asked to find the test statistic.
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