Q1. Which of the following statements about the variance of a normally distributed population is least accurate?
A) The Chi-squared distribution is a symmetric distribution.
B) The test of whether the population variance equals σ02 requires the use of a Chi-squared distributed test statistic, [(n ? 1)s2] / σ02.
C) A test of whether the variance of a normally distributed population is equal to some value σ02, the hypotheses are: H0: σ2 = σ02, versus Ha: σ2 ≠ σ02.
Correct answer is A)
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).
Q2. A test of the population variance is equal to a hypothesized value requires the use of a test statistic that is:
A) F-distributed.
B) Chi-squared distributed.
C) t-distributed.
Correct answer is B)
In tests of whether the variance of a population equals a particular value, the chi-squared test statistic is appropriate.
Q3. A munitions manufacturer claims that the standard deviation of the powder packed in its shotgun shells is 0.1% 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%. What is the Chi-squared value, and what are the critical values at a 95% confidence level, respectively?
A) 72; 32.357 and 71.420.
B) 72; 34.764 and 67.505.
C) 70; 34.764 and 79.490.
Correct answer is A)
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% 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.
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发表于 2009-6-2 16:22
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