In Exercises 7–12, find the critical value(s) and rejection re...

Question

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Right-tailed test, n=10,α=0.10

Accepted Answer

All right. Hello, everyone. So this question says, a nutritionist is testing whether the variability in daily calcium intake among adults has increased compared to the known standard deviation. The population is assumed to be normally distributed. She performs a right-tailed chi square test using a random sample of 10 adults. She chooses a significance level of 0.10. What is the critical value and the rejection region for this right-tailed chi square test? And here we've got 4 different answer choices labeled A through D. So first and foremost, this is a right-tailed chi square test for variants or standard deviation. So the first thing to do is to identify the degrees of freedom, which is based on the sample size. Recall the degrees of freedom. is equal to N subtracted by 1, where N is the sample size. So here, 10 subtracted by 1 gives you 9 degrees of freedom. Then It's important to recognize the type of test that you're taking into account. This is a right-tailed test, which means that we're testing if the variability is greater than the hypothesized value. Greater as in to the right of the hypothesized value in a number line. Because of this, we have to find the chi square critical value that leaves 10% of the area in the right tail of the chi square distribution with 9 degrees of freedom. So, on to the critical value. To find this critical value, you first go to the row corresponding to 9 degrees of freedom, and then find the column corresponding to alpha equals 0.10 in the right tail area. Once you find this value. I swear Of 0.10 and 9 degrees of freedom, equals 14.684. So What this means is that the probability of observing a chi square value greater than 14.684, when the null hypothesis is true, is 0.10. So now, for the rejection region, since we already have the critical value. Recall that this is a right-tailed test. So we're looking to see. If the variability is greater than what's been stated, so. Chi square would then have to be greater than 14.684 in order to reject the null hypothesis. And there you have it. Now we've arrived at our final answer. Our critical value is 14.684, which means that the rejection region. is when chi square is greater than 14.684. And this corresponds to option D in the multiple choice. And so with that being said, thank you so very much for watching, and I hope you found this helpful.

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

Right-tailed test, n=10,α=0.10

Key Concepts

Chi-Square Test

Critical Value

Rejection Region

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