1.A test of the population variance is equal to a hypothesized value requires the use of a test statistic that is:

A)   t-distributed.

B)   z-distributed.

C)   Chi-squared distributed.

D)   F-distributed.

2.Which of the following statements about the variance of a normally distributed population is FALSE?

A)   The test of whether the population variance equals σ₀² requires the use of a Chi-squared distributed test statistic, [(n-1)s²] / σ₀².

B)   A test of whether the variance of a normally distributed population is equal to some value σ₀², the hypotheses are: H₀: σ²= σ₀², versus H_a: σ² ≠ σ₀².

C)   The alternative hypothesis in a test concerning the value of the variance of a normally distributed population may be one or two-sided.

D)   The Chi-squared distribution is a symmetric distribution.

3.A munitions manufacturer claims that the standard deviation of the powder packed in its shotgun shells is 0.1 percent of the stated nominal amount of powder. A sport clay association has reviewed a sample of 51 shotgun shells and found a standard deviation of 0.12 percent. What is the Chi-squared value, and what are the critical values at a 95 percent confidence level?

A)                           72          34.764 and 67.505

B)                           70          34.764 and 79.490

C)                           72          32.357 and 71.420

D)                           72          67.505 and 79.490

答案和详解如下：

1.A test of the population variance is equal to a hypothesized value requires the use of a test statistic that is:

A)   t-distributed.

B)   z-distributed.

C)   Chi-squared distributed.

D)   F-distributed.

The correct answer was C)    

In tests of whether the variance of a population equals a particular value, the chi-squared test statistic is appropriate.

2.Which of the following statements about the variance of a normally distributed population is FALSE?

A)   The test of whether the population variance equals σ₀² requires the use of a Chi-squared distributed test statistic, [(n-1)s²] / σ₀².

B)   A test of whether the variance of a normally distributed population is equal to some value σ₀², the hypotheses are: H₀: σ²= σ₀², versus H_a: σ² ≠ σ₀².

C)   The alternative hypothesis in a test concerning the value of the variance of a normally distributed population may be one or two-sided.

D)   The Chi-squared distribution is a symmetric distribution.

The correct answer was D)

The Chi-squared distribution is not symmetrical, which means that the critical values will not be numerically equidistant from the center of the distribution, though the probability on either side of the critical values will be equal (that is, if there is a 5% level of significance and a two-sided test, 2.5% will lie outside each of the two critical values.

3.A munitions manufacturer claims that the standard deviation of the powder packed in its shotgun shells is 0.1 percent of the stated nominal amount of powder. A sport clay association has reviewed a sample of 51 shotgun shells and found a standard deviation of 0.12 percent. What is the Chi-squared value, and what are the critical values at a 95 percent confidence level?

Chi-square

Critical Values

A)                           72          34.764 and 67.505

B)                           70          34.764 and 79.490

C)                           72          32.357 and 71.420

D)                           72          67.505 and 79.490

The correct answer was C)

To compare standard deviations we use a Chi-square statistic. X² = (n – 1)s² / σ₀² = 50(0.0144) / 0.01 = 72. With 50 df, the critical values at the 95 percent confidence level are 32.357 and 71.420. Since the Chi-squared value is outside this range, we can reject the hypothesis that the standard deviations are the same.