Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A)  σ 2 ≥ 7. 
C)  σ 2 ≥ 49. 
A)  σ 2 ≥ 7. 
C)  σ 2 ≥ 49. B

Question 3

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)

Accepted Answer

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

Question 4

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

Accepted Answer

A)    $\chi _ { .05 } ^ { 2 }$ < $\chi ^ { 2 }$ < $\chi _ { .95 } ^ { 2 }$  . 
B)  $\chi _ { .10 } ^ { 2 }$ $\le$$\chi ^ { 2 }$ $\le$ $\chi _ { .90 } ^ { 2 }$ . 
C)    $\chi _ { .95 } ^ { 2 }$ $\le$ $\chi ^ { 2 }$ $\le$ $\chi _ { .05 } ^ { 2 }$  . 
D)    $\chi _ { .90 } ^ { 2 }$ < $\chi ^ { 2 }$ < $\chi _ { .10 } ^ { 2 }$  . 
A)    $\chi _ { .05 } ^ { 2 }$ < $\chi ^ { 2 }$ < $\chi _ { .95 } ^ { 2 }$  . 
B)  $\chi _ { .10 } ^ { 2 }$ $\le$$\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 5

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

Accepted Answer

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

Question 6

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​

Accepted Answer

A)  11.808 and 49.645. 
B)  ​14.573 and 43.195. 
C)  ​16.151 and 40.113. 
D)  ​15.308 and 44.461. 
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 7

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

Accepted Answer

A)  1715.101 to 4055.589. 
B)  1596.458 to 4466.679. 
C)  39.956 to 66.833. 
D)  41.393 to 63.684. 
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 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

A)  27.99 and 79.49. 
B)  32.357 and 71.420. 
C)  34.764 and 67.505. 
D)  12.8786 and 46.9630. 
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 12

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

Accepted Answer

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

Question 13

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)

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Which of the following rejection rules is proper?

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

A)  H0: σ2 0: s2 ≥ 1.44. 
C)  H0: σ 0: σ2 ≥ 1.44. 
A)  H0: σ2 0: s2 ≥ 1.44. 
C)  H0: σ 0: σ2 ≥ 1.44.

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

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

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)

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

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

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

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

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 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

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

Consider the following hypothesis problem. n=30 :=500 s2=625 :?500 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)

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

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

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. Sample A Sample B n 11 10 12.1 5 The test statistic for this problem equals

Which of the following rejection rules is proper?

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

Consider the following sample information from Population A and Population B. Sample A Sample B n 24 16 32 38 We want to test the hypothesis that the population variances are equal.At the 10% level of significance, the null hypothesis

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

Data and Statistics

Descriptive Statistics: Tabulargraphical

Descriptive Statistics: Numerical

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Filters

Exam 11: Inferences About Population Variances

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

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

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)

There is a .90 probability of obtaining a χ2\chi ^ { 2 }χ2 value such that

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

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

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

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 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

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

Consider the following hypothesis problem. n=30 :=500 s2=625 :?500 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)

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

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

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. Sample A Sample B n 11 10 12.1 5 The test statistic for this problem equals

Which of the following rejection rules is proper?

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

Consider the following sample information from Population A and Population B. Sample A Sample B n 24 16 32 38 We want to test the hypothesis that the population variances are equal.At the 10% level of significance, the null hypothesis

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

Data and Statistics

Descriptive Statistics: Tabulargraphical

Descriptive Statistics: Numerical

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Filters

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

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

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

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

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

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

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