Chapter 11: Inferences About Population Variances

The sampling distribution of is a normal probability distribution.
1. True
2. False
The random variable for the chi-square probability distribution may not assume negative values.
1. True
2. False
The chi-square probability distribution is symmetric.
1. True
2. False
The chi-square value with area to the right of .10 with 16 degrees of freedom is
1. 9.31223
2. 22.3072
3. 23.5418
4. 26.2962
The chi-square value with area to the left of .05 with 12 degrees of freedom is
1. 4.57481
2. 5.22603
3. 19.6751
4. 21.0261
When a sample variance of 25 is obtained from a sample of 10 items from a normal population, the 80% confidence interval for a population variance is
1. 12.3 to 57.1
2. 13.3 and 67.7
3. 14.1 to 46.25
4. 15.3 to 53.98
A maximum acceptable standard deviation for a process is 0.5. To test this, which would be the appropriate null hypothesis?
1. μ > 0.5
2. σ < 0.5
3. σ ≤ 0.5
4. σ ≠ 0.5
5. none of the above
A maximum acceptable standard deviation for a process is 0.5. A sample of size 20 is taken from a normal distribution, giving s = 0.6. The appropriate decision with α = .05 is
1. reject the null hypothesis
2. do not reject the null hypothesis
For the F distribution, the number of degrees of freedom in the numerator must be greater than or equal to the number of degrees of freedom in the denominator.
1. True
2. False
When a sample variance of 25 is obtained from a sample of 10 items from a normal population, the 90% confidence interval for a population variance is
1. 12.3 to 57.1
2. 13.3 and 67.7
3. 14.1 to 46.25
4. 15.3 too 53.98
The sampling distribution of the ratio of independent sample variances from two normally distributed populations with equal variances is the
1. chi-square distribution
2. normal distribution
3. F distribution
4. t distribution
The F value with area to the right of .025 with numerator degrees of freedom 12 and denominator degrees of freedom 10 is
1. 2.91
2. 3.37
3. 3.62
4. 4.71
These sample results were obtained for independent random samples from two normally distributed populations.

Using a .05 level of significance, one critical value needed to use the F test for the equality of the population variances is
1. 2.59
2. 3.01
3. 3.12
4. 3.89
These sample results were obtained for independent random samples from two normally distributed populations.

The value of the statistic F is
1. .13
2. .5
3. 1.12
4. 1.25
These sample results were obtained for independent random samples from two normally distributed populations.

Using a .05 level of significance, which conclusion would be reached for these data?
1. There is a statistically significant difference between the variances of the two populations.
2. There is no statistically significant difference between the variances of the two populations.
3. Insufficient data - can't tell in this case.