Deck 11: Inferences About Population Variances

Question 1

To avoid the problem of not having access to Tables of F distribution when F values are needed for the lower tail, the numerator of the test statistic for a two-tailed test should be the one with

A) the larger sample size.
B) the smaller sample size.
C) the larger sample variance.
D) the smaller sample variance.

Answer 1

the larger sample variance.

Question 2

The value of F_.05 with 8 numerator and 19 denominator degrees of freedom is

A) 2.48.
B) 2.58.
C) 3.63.
D) 2.96.

Answer 2

2.48.

Question 3

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes.A 95% confidence interval estimate for the variance of service times for all their new automobiles is

A) 8.576 to 39.794.
B) 9.46 to 34.09.
C) 2.144 to 9.948.
D) 2.93 to 6.31.

Answer 3

8.576 to 39.794.

Question 4

A sample of 21 observations yielded a sample variance of 16.If we want to test H₀: σ² = 16, the test statistic is

A) 20.
B) 21.
C) 5.
D) 50.

Question 5

The producer of a certain bottling equipment claims that the variance of all their filled bottles is .027 or less.A sample of 30 bottles showed a standard deviation of .2 ounces.The p-value for the test is

A) between .025 to .05.
B) between .05 to .10.
C) .05.
D) .025.

Question 6

A sample of 41 observations yielded a sample standard deviation of 5.If we want to test H₀: σ² = 20, the test statistic is

A) 100.75.
B) 10.
C) 51.25.
D) 50.

Question 7

The random variable for a chi-square distribution may assume

A) any value between -1 to 1.
B) any value between -∞ to +∞.
C) any negative value.
D) any value greater than zero.

Question 8

A sample of n observations is taken from a normal population.The appropriate chi-square distribution has

A) n degrees of freedom.
B) n - 1 degrees of freedom.
C) n - 2 degrees of freedom.
D) n - 3 degrees of freedom.

Question 9

A sample of 20 cans of tomato juice showed a standard deviation of .4 ounces.A 95% confidence interval estimate of the variance for the population is

A) .2313 to .8533.
B) .2224 to .7924.
C) .3042 to .5843.
D) .0925 to .3413.

Question 10

The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 6 minutes.A 95% confidence interval estimate for the standard deviation of the service times (in minutes) for all their new automobiles is

A) 16.047 to 45.722.
B) 4.778 to 8.066.
C) 2.93 to 6.31.
D) 22.833 to 65.059.

Question 11

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is .05 or less.The null hypothesis in a test to confirm the claim would be written as

A) H₀: σ² ≥ .05.
B) H₀: σ² > .05.
C) H₀: σ² < .05.
D) H₀: σ² ≤ .05.

Question 12

The symbol used for the variance of the population is

A) σ.
B) σ².
C) s.
D) s².

Question 13

The sampling distribution used when making inferences about a single population's variance is

A) an F distribution.
B) a t distribution.
C) a chi-square distribution.
D) a normal distribution.

Question 14

We are interested in testing whether the variance of a population is significantly less than 1.44.The null hypothesis for this test is

A) H₀: σ² < 1.44.
B) H₀: s² ≥ 1.44.
C) H₀: σ < 1.20.
D) H₀: σ² ≥ 1.44.

Question 15

For an F distribution, the number of degrees of freedom for the numerator

A) must be larger than the number of degrees of freedom for the denominator.
B) must be smaller than the number of degrees of freedom for the denominator.
C) must be equal to the number of degrees of freedom for the denominator.
D) can be larger, smaller, or equal to the number of degrees of freedom for the denominator.

Question 16

The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is .1 ounces or less.A sample of 20 bottles showed a standard deviation of .11 ounces.The test statistic to test the claim is

A) 2.3.
B) 22.99.
C) 4.85.
D) 24.2.

Question 17

A sample of 51 elements is selected to estimate a 95% confidence interval for the variance of the population.The chi-square values to be used for this interval estimation are

A) 27.99 and 79.49.
B) 32.357 and 71.420.
C) 34.764 and 67.505.
D) 12.8786 and 46.9630.

Question 18

The symbol used for the variance of the sample is

A) σ.
B) σ².
C) s.
D) s².

Question 19

Which of the following has an F distribution?

A) (n - 1)s/?.
B) s₁/s₂.
C) (n - 1)s₁/s₂.
D) $s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }$ .

Question 20

Which of the following has a chi-square distribution?

A) (n - 1)σ²/s².
B) (n - 1)σ/s.
C) (n - 1)s/σ.
D) (n - 1)s²/σ².

Question 21

The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of 25 is

A) 33.196.
B) 36.415.
C) 39.364.
D) 37.652.

Question 22

A sample of 21 elements is selected to estimate a 90% confidence interval for the variance of the population.The chi-square value(s) to be used for this interval estimation is(are)

A) 31.410.
B) 12.443.
C) 10.851 and 31.410.
D) 12.443 and 28.412.

Question 23

A sample of 61 observations yielded a sample standard deviation of 6.If we want to test H₀: σ² = 40, the test statistic is

A) 54.
B) 9.15.
C) 54.90.
D) 9.

Question 24

The critical value of F using α = .05 when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is

A) 2.45.
B) 2.94.
C) 2.37.
D) 2.10.

Question 25

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

A) chi-square distribution.
B) normal distribution.
C) F distribution.
D) t distribution.

Question 26

The sampling distribution of the quantity (n - 1)s2/σ² is the

A) chi-square distribution.
B) normal distribution.
C) F distribution.
D) t distribution.

Question 27

We are interested in testing to see if the variance of a population is less than 7.The correct null hypothesis is

A) σ < 7.
B) σ² ≥ 7.
C) σ < 49.
D) σ² ≥ 49.

Question 28

For a sample size of 21 at 95% confidence, the chi-square values needed for interval estimation are

A) 9.591 and 34.170.
B) 2.700 and 19.023.
C) 8.260 and 37.566.
D) 10.283 and 35.479.

Question 29

The 90% confidence interval estimate of a population standard deviation when a sample variance of 50 is obtained from a sample of 15 items is

A) 26.8 to 124.356.
B) 5.177 to 11.152.
C) 5.436 to 10.321.
D) 29.555 to 106.529.

Question 30

The value of F_.01 with 9 numerator and 20 denominator degrees of freedom is

A) 2.39.
B) 2.94.
C) 2.91.
D) 3.46.

Question 31

The 99% confidence interval estimate for a population variance when a sample standard deviation of 12 is obtained from a sample of 10 items is

A) 4.589 to 62.253.
B) 46.538 to 422.171.
C) 54.941 to 746.974.
D) 62.042 to 562.895.

Question 32

The chi-square value for a one-tailed (lower tail) test when the level of significance is .1 and the sample size is 15 is

A) 21.064.
B) 23.685.
C) 7.790.
D) 6.571.

Question 33

We are interested in testing whether the variance of a population is significantly more than 625.The null hypothesis for this test is

A) H₀: σ² > 625.
B) H₀: σ² ≤ 625.
C) H₀: σ² ≥ 625.
D) H₀: σ² ≤ 25.

Question 34

A sample of 60 items from population 1 has a sample variance of 8 while a sample of 40 items from population 2 has a sample variance of 10.If we want to test whether the variances of the two populations are equal, the test statistic will have a value of

A) .8.
B) 1.56.
C) 1.5.
D) 1.25.

Question 35

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces.We are interested in testing whether the variance of the population is significantly more than .003.The p-value for this test is

A) .05.
B) greater than .10.
C) less than .10.
D) zero.

Question 36

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces.We are interested in testing whether the variance of the population is significantly more than .003.The test statistic is

A) 1.2.
B) 31.2.
C) 30.
D) 500.

Question 37

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

A) 14.14 to 174.94.
B) 243.086 to 453.520.
C) 16.42 to 194.35.
D) 254.419 to 429.203.

Question 38

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces.We are interested in testing whether the variance of the population is significantly more than .003.The null hypothesis is

A) s² > .003.
B) s² ≤ .003.
C) σ² > .003.
D) σ² ≤ .003.

Question 39

A random sample of 31 sales charge showed a sample standard deviation of $50.A 90% confidence interval estimate of the population standard deviation is

A) 1715.101 to 4055.589.
B) 1596.458 to 4466.679.
C) 39.956 to 66.833.
D) 41.393 to 63.684.

Question 40

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces.We are interested in testing whether the variance of the population is significantly more than .003.At the .05 level of significance, the null hypothesis

A) should be rejected.
B) should not be rejected.
C) should be revised.
D) should not be tested.

Question 41

Consider the following sample information from Population A and Population B. $$\begin{array} { c c } &\text { Sample A } & \text { Sample B } \\n&24 & 16 \\s^2&32 & 38\end{array}$$
We want to test the hypothesis that the population variances are equal.At the 10% level of significance, the null hypothesis

A) should be rejected.
B) should not be rejected.
C) should be revised.
D) should not be tested.

Question 42

Consider the following hypothesis problem. $$\begin{array} { l l } n = 14 & H _ { 0 } : \sigma ^ { 2 } \leq 410 \\s = 20 & H _ { \mathrm { a } } : \sigma ^ { 2 } > 410\end{array}$$ The null hypothesis is to be tested at the 5% level of significance.The critical value(s) from the chi-square distribution table is(are)

A) 22.362.
B) 23.685.
C) 5.009 and 24.736.
D) 5.629 and 26.119.

Question 43

Consider the following hypothesis problem. $$\begin{array} { l l } n = 30 & H _ { 0 } : \sigma ^ { 2 } = 500 \\s 2 = 625 & H _ { \mathrm { a } } : \sigma ^ { 2 } ? 500\end{array}$$ The null hypothesis is to be tested at the 5% level of significance.The critical value(s) from the chi-square distribution table is(are)

A) 42.557.
B) 43.773.
C) 16.047 and 45.722.
D) 16.791 and 46.979.

Question 44

To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let​ the

A) smaller sample variance be the numerator of the test statistic.
B) larger sample variance be the numerator of the test statistic.
C) sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic.
D) sample variance from the population with the larger hypothesized variance be the numerator of the test statistic.

Question 45

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population.The chi-square values to be used for this interval estimation are​

A) 11.808 and 49.645.
B) ​14.573 and 43.195.
C) ​16.151 and 40.113.
D) ​15.308 and 44.461.

Question 46

There is a .90 probability of obtaining a $\chi ^ { 2 }$ value such that

A) $\chi _ { .05 } ^ { 2 }$ < $\chi ^ { 2 }$ < $\chi _ { .95 } ^ { 2 }$ .
B) $\chi _ { .10 } ^ { 2 }$ $\le$$\chi ^ { 2 }$ $\le$ $\chi _ { .90 } ^ { 2 }$ .
C) $\chi _ { .95 } ^ { 2 }$ $\le$ $\chi ^ { 2 }$ $\le$ $\chi _ { .05 } ^ { 2 }$ .
D) $\chi _ { .90 } ^ { 2 }$ < $\chi ^ { 2 }$ < $\chi _ { .10 } ^ { 2 }$ .

Question 47

Which of the following rejection rules is proper?

A) Reject H₀ if p-value $\le$ F
B) Reject H₀ if F $\le$ F
C) Reject H₀ if p-value $\ge$$\alpha$ /2.
D) Reject H₀ if F $\ge$ F11ef1cb7_2c09_13ea_98f1_27c3120dec2e_TB1213_11

Question 48

​Consider the following hypothesis problem. n = 30
H₀: σ² = 500
S2 = 625
H_a: σ² ≠ 500
​
At the 5% level of significance, the null hypothesis

A) ​should be rejected.
B) ​should not be rejected.
C) ​should be revised.
D) should not be tested.

Question 49

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B.
$\begin{array}{ll}&\text { Sample A } & \text { Sample B } \\n&11 & 10 \\s^2&12.1 & 5\end{array}$
The p-value is approximately

A) .10.
B) .05.
C) .025.
D) .01.

Question 50

Consider the following hypothesis problem. $\begin{array}{lll}n=23 & s^{2}=60 & H_{0}: \sigma^{2}=66 \\&& H_{\mathrm{a}}: \sigma^{2}>66\end{array}$
If the test is to be performed at the 5% level, the critical value(s) from the chi-square distribution table is(are)

A) 10.982 and 36.781.
B) 12.338 and 33.924.
C) 12.338.
D) 33.924.

Question 51

Consider the following hypothesis problem. $\begin{array}{lll}n=23 & s^{2}=60 & H_{0}: \sigma^{2}=66 \\&& H_{\mathrm{a}}: \sigma^{2}>66\end{array}$
The test statistic has a value of

A) 20.91.
B) 24.20.
C) 24.00.
D) 20.00.

Question 52

Consider the following hypothesis problem. $$\begin{array} { l l } n = 14 & H _ { 0 } : \sigma ^ { 2 } \leq 410 \\s = 20 & H _ { \mathrm { a } } : \sigma ^ { 2 } > 410\end{array}$$ The test statistic equals

A) .63.
B) 12.68.
C) 13.33.
D) 13.68.

Question 53

Consider the following hypothesis problem. $\begin{array}{lll}n=23 & s^{2}=60 & H_{0}: \sigma^{2}=66 \\&& H_{\mathrm{a}}: \sigma^{2}>66\end{array}$
If the test is to be performed at the .05 level of significance, the null hypothesis

A) should be rejected.
B) should not be rejected.
C) should be revised.
D) should not be tested.

Question 54

Consider the following sample information from Population A and Population B. $$\begin{array} { c c } &\text { Sample A } & \text { Sample B } \\n&24 & 16 \\s^2&32 & 38\end{array}$$
We want to test the hypothesis that the population variances are equal.The null hypothesis is to be tested at the 10% level of significance.The critical value from the F distribution table is

A) 2.11.
B) 2.13.
C) 2.24.
D) 2.29.

Question 55

Consider the following hypothesis problem. $$\begin{array} { l l } n = 14 & H _ { 0 } : \sigma ^ { 2 } \leq 410 \\s = 20 & H _ { \mathrm { a } } : \sigma ^ { 2 } > 410\end{array}$$ At the 5% level of significance, the null hypothesis

A) should be rejected
B) should not be rejected
C) should be revised.
D) should not be tested.

Question 56

​In practice, the most frequently encountered hypothesis test about a population variance is a

A) ​one-tailed test, with rejection region in the lower tail.
B) ​one-tailed test, with rejection region in the upper tail.
C) ​two-tailed test, with equal-size rejection regions.
D) ​two-tailed test, with unequal-size rejection regions.

Question 57

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. $\begin{array}{ll}&\text { Sample A } & \text { Sample B } \\n&11 & 10 \\s^2&12.1 & 5\end{array}$
The test statistic for this problem equals

A) .4132.
B) 1.1.
C) 2.42.
D) 2.

Question 58

Consider the following sample information from Population A and Population B. $$\begin{array} { c c } &\text { Sample A } & \text { Sample B } \\n&24 & 16 \\s^2&32 & 38\end{array}$$
We want to test the hypothesis that the population variances are equal.The test statistic for this problem equals

A) .67.
B) .84.
C) 1.19.
D) 1.50.

Question 59

Consider the following hypothesis problem. $\begin{array}{lll}n=23 & s^{2}=60 & H_{0}: \sigma^{2}=66 \\&& H_{\mathrm{a}}: \sigma^{2}>66\end{array}$
The p-value is

A) less than .025.
B) between .025 and .05.
C) between .05 and .10.
D) greater than .10.

Question 60

​Consider the following hypothesis problem. n = 30
H₀: σ² = 500
S2 = 625
H_a: σ² ≠ 500
​
​The test statistic equals

A) ​23.20.
B) ​24.00.
C) ​36.25.
D) ​37.50.