Q: A sporting goods manufacturer claims the variance of fishing line strength is $$15.9. A $$sample of $$n = 15$$ spools has a variance of $$21.8. $$What is the test statistic for this hypothesis test?

$$\$$chi^2$$ = \frac{(15-1) \times 21.8}{15.9}$$

Q: A sample of $$n = 20$$ has a sample variance of $$5.2. $$You are testing $$H_0$$: \$$sigma^2 = 4$ at $$\alpha = 0.05$$. What is the test statistic?

$$\$$chi^2$$ = \frac{19 \times 5.2}{4}$$

Question 1

Which of the following is a necessary assumption for using the chi-square test for variance or standard deviation?

Accepted Answer

The population must be normally distributed.

Question 2

A dairy company claims the variance of fat in milk is no more than $$0.25. $$You collect a sample of $$n = 41$$ containers with a sample variance of $$0.27. $$What is the correct null hypothesis for this test?

Accepted Answer

$$H_0$$: \$$sigma^2$$ \leq 0.25$$

Question 3

What is the formula for the chi-square test statistic when testing a population variance?

Accepted Answer

$$\$$chi^2$$ = \frac{(n-1)s^2$}{\$$sigma^2$$}$$

Question 4

If you are conducting a left-tailed chi-square test for variance with $$n = 11$$ and $$\alpha = 0.01$$, what are the degrees of freedom?

Accepted Answer

$$df = 10$$

Question 5

A company claims the standard deviation of call transfer times is less than $$1.4$$ minutes. A sample of $$n = 25$$ calls has $$s = 1.1$$ minutes. What is the alternative hypothesis?

Accepted Answer

$$H_1$$: \sigma \u003c 1.4$$

Question 6

Which of the following best describes the rejection region for a right-tailed chi-square test at significance level $$\alpha$$?

Accepted Answer

$$\$$chi^2$$ \u003e \$$chi^2$$_{\alpha, df}$$

Question 7

In a two-tailed chi-square test with $$n = 9$$ and $$\alpha = 0.05$$, what are the areas in each tail?

Accepted Answer

0.025 in each tail

Question 8

A sporting goods manufacturer claims the variance of fishing line strength is $$15.9. A $$sample of $$n = 15$$ spools has a variance of $$21.8. $$What is the test statistic for this hypothesis test?

Accepted Answer

$$\$$chi^2$$ = \frac{(15-1) 	imes 21.8}{15.9}$$

Question 9

Which of the following scenarios would require a two-tailed chi-square test?

Accepted Answer

Testing if the population variance is different from a specified value

Question 10

Why is it important to check that the population is normally distributed before using the chi-square test for variance?

Accepted Answer

The chi-square test is not robust to violations of normality, which can affect the validity of the results.

Question 11

A researcher wants to test if the variance of exam scores in a class is greater than $$16. $$Which of the following is the correct set of hypotheses?

Accepted Answer

$$H_0$$: \$$sigma^2$$ \leq 16$$, H_1$: \$$sigma^2$$ \u003e 16$$

Question 12

If the calculated chi-square test statistic falls in the rejection region, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 13

Which of the following is NOT a step in conducting a chi-square test for variance?

Accepted Answer

Calculate the sample mean.

Question 14

A sample of $$n = 20$$ has a sample variance of $$5.2. $$You are testing $$H_0$$: \$$sigma^2 = 4$ at $$\alpha = 0.05$$. What is the test statistic?

Accepted Answer

$$\$$chi^2$$ = \frac{19 	imes 5.2}{4}$$

Question 15

In a left-tailed chi-square test, what does it mean if the test statistic is less than the critical value?

Accepted Answer

Reject the null hypothesis.

Hypothesis Testing for Variance and Standard Deviation: Chi-Square Tests

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