Question 1

In testing for equality of two standard deviations using the $F$ statistic of $\alpha=0.02$, the $F$ table value that must be exceeded to reject the null hypothesis is given by the symbol __________.

Accepted Answer

The answer of In testing for equality of two standard...

Question 2

The hypothesis that two population standard deviations are equal can be rejected at the $10 \%$ level of significance if

Accepted Answer

A)  $F>F_{0.10}$ 
B)  $F>F_{0.05}$. 
C)  $F>F_{0.20}$. 
D)

Question 3

The symbol $X^{2}$ has which of the following properties?

Accepted Answer

A)  It equals $\mathrm{X}^{2} \alpha$. 
B)  The area to its right equals $\alpha$. 
C)  It has $n-1$ degrees of freedom. 
D)  The area to its left equals $\alpha / 2$.

Question 4

In order to test the hypothesis that a population $\sigma$ is a specified constant, it is never necessary to know the mean of the sample.

Accepted Answer

A) True 
 B)False

Question 5

If $s_{1}^{2}=30$ and $s_{2}^{2}=20$, then the $F$ ratio we use is __________.

Accepted Answer

The answer of If $s_{1}^{2}=30$ and $s_{2}^{2}=20$, then the $F$...

Question 6

A man who needs an operation would like to evaluate the variation in survival rates in different hospitals for his type of operation. He hypothesizes that the standard deviation of survival rates at all hospitals is 0.08 . Test this hypothesis against the alternative hypothesis $\sigma \neq 0.08$ if a random sample of 12 hospitals produces a standard deviation of 0.11 . Use $\alpha=0.10$.

Accepted Answer

The answer of A man who needs an operation would...

Question 7

A vending machine company wants to limit the variation in the number of ounces of soda that their machine dispenses into each cup. Use the 0.01 level of significance to test the null hypothesis $\sigma=0.12$ ounces against the alternative hypothesis $\sigma>0.12$ ounces based on a random sample of size $n=15$ cups for which $s=0.18$.

Accepted Answer

The answer of A vending machine company wants to limit...

Question 8

An $F$ ratio is the ratio of two population standard deviations.

Accepted Answer

A) True 
 B)False

Question 9

Calculate the $F$ ratio for the set of data and compare it to the appropriate tabled value. Make a decision concerning the null hypothesis of equal population standard deviations.
-$s_{1}=5 \quad n_{1}=13$
$s_{2}=9 \quad n_{2}=10$
$\alpha=0.10$

Accepted Answer

The answer of Calculate the $F$ ratio for the set...

Question 10

Finding a large-sample confidence interval for $\sigma$ requires the use of the normal distribution, whereas finding a small-sample confidence interval for $\sigma$ requires the use of $t$ distribution.

Accepted Answer

A) True 
 B)False

Question 11

A random sample of 11 copies of a particular mechanical component has a mean length of 5 inches with a standard deviation of $\mathbf{0 . 6 0}$.
-Find a $90 \%$ confidence interval for the population variance.

Accepted Answer

The answer of A random sample of 11 copies of...

Question 12

Find the critical value needed to test the null hypothesis that $\sigma=40$ against the alternative hypothesis that $\sigma>$ 40 at $\alpha=0.01$ using a sample of size $n=80$.

Accepted Answer

The answer of Find the critical value needed to test...

Question 13

To find a $90 \%$ confidence interval for the standard deviation from a small sample, we use the values

Accepted Answer

A)  $X_{0.90}^{2}$ and $X_{0.10}^{2}$. 
B)  $X_{0.95}^{2}$ and $X_{0.05}^{2}$. 
C)  $X_{0.975}^{2}$ and $X_{0.025}^{2}$. 
D)  only $X_{0.90}^{2}$.

Question 14

The procedure used to evaluate the null hypothesis $\sigma_{1}=\sigma_{2}$ is the same as the procedure used to evaluate the null hypothesis $\sigma=\sigma_{0}$ where $\sigma_{0}$ is a constant.

Accepted Answer

A) True 
 B)False

Question 15

A computed $X^{2}$ value that is larger than the $X_{\alpha / 2}^{2}$ value allows us to reject the null hypothesis that __________ is based on a __________.

Accepted Answer

A)  $\sigma=\sigma_{0}$, small sample 
B)  $\sigma=\sigma_{0}$, large sample 
C)  $\sigma_{1}=\sigma_{2}$, small sample 
D)  $\sigma_{1}=\sigma_{2}$, large sample

Question 16

To test the hypothesis that two population standard deviations are equal, we use which of the following distributions?

Accepted Answer

A)  $F$ 
B)  chi-square 
C)  normal 
D)  $t$

Question 17

In a random sample of nine gasoline stations in New York City, the prices per gallon of unleaded gas have a standard deviation of $\$ 0.08$ per gallon. In a random sample of 14 gasoline stations in Chicago, the prices per gallon have a standard deviation of $\$ 0.03$ per gallon. Use the $10 \%$ significance level to test the null hypothesis that the price per gallon of gasoline is equally variable in the two cities.

Accepted Answer

The answer of In a random sample of nine gasoline...

Question 18

A random sample of 11 copies of a particular mechanical component has a mean length of 5 inches with a standard deviation of $\mathbf{0 . 6 0}$.
-Find a $95 \%$ confidence interval for the population standard deviation.

Accepted Answer

The answer of A random sample of 11 copies of...

Question 19

The $F$ ratio can be used to evaluate the null hypothesis that the population standard deviation equals a given constant.

Accepted Answer

A) True 
 B)False

Exam 13: Tests of Hypotheses: Standard Deviations

In testing for equality of two standard deviations using the $F$ statistic of $\alpha=0.02$ , the $F$ table value that must be exceeded to reject the null hypothesis is given by the symbol __________.

The hypothesis that two population standard deviations are equal can be rejected at the $10 \%$ level of significance if

The symbol $X^{2}$ has which of the following properties?

In order to test the hypothesis that a population $\sigma$ is a specified constant, it is never necessary to know the mean of the sample.

If $s_{1}^{2}=30$ and $s_{2}^{2}=20$ , then the $F$ ratio we use is __________.

An $F$ ratio is the ratio of two population standard deviations.

Calculate the $F$ ratio for the set of data and compare it to the appropriate tabled value. Make a decision concerning the null hypothesis of equal population standard deviations. - $s_{1}=5 \quad n_{1}=13$ $s_{2}=9 \quad n_{2}=10$ $\alpha=0.10$

Finding a large-sample confidence interval for $\sigma$ requires the use of the normal distribution, whereas finding a small-sample confidence interval for $\sigma$ requires the use of $t$ distribution.

A random sample of 11 copies of a particular mechanical component has a mean length of 5 inches with a standard deviation of $\mathbf{0 . 6 0}$ . -Find a $90 \%$ confidence interval for the population variance.

Find the critical value needed to test the null hypothesis that $\sigma=40$ against the alternative hypothesis that $\sigma>$ 40 at $\alpha=0.01$ using a sample of size $n=80$ .

To find a $90 \%$ confidence interval for the standard deviation from a small sample, we use the values

The procedure used to evaluate the null hypothesis $\sigma_{1}=\sigma_{2}$ is the same as the procedure used to evaluate the null hypothesis $\sigma=\sigma_{0}$ where $\sigma_{0}$ is a constant.

A computed $X^{2}$ value that is larger than the $X_{\alpha / 2}^{2}$ value allows us to reject the null hypothesis that is based on a .

To test the hypothesis that two population standard deviations are equal, we use which of the following distributions?

A random sample of 11 copies of a particular mechanical component has a mean length of 5 inches with a standard deviation of $\mathbf{0 . 6 0}$ . -Find a $95 \%$ confidence interval for the population standard deviation.

The $F$ ratio can be used to evaluate the null hypothesis that the population standard deviation equals a given constant.

Exam 13: Tests of Hypotheses: Standard Deviations

In testing for equality of two standard deviations using the FFF statistic of α=0.02\alpha=0.02α=0.02 , the FFF table value that must be exceeded to reject the null hypothesis is given by the symbol __________.

The hypothesis that two population standard deviations are equal can be rejected at the 10%10 \%10% level of significance if

The symbol X2X^{2}X2 has which of the following properties?

In order to test the hypothesis that a population σ\sigmaσ is a specified constant, it is never necessary to know the mean of the sample.

If s12=30s_{1}^{2}=30s12​=30 and s22=20s_{2}^{2}=20s22​=20 , then the FFF ratio we use is __________.

An FFF ratio is the ratio of two population standard deviations.

Finding a large-sample confidence interval for σ\sigmaσ requires the use of the normal distribution, whereas finding a small-sample confidence interval for σ\sigmaσ requires the use of ttt distribution.

A random sample of 11 copies of a particular mechanical component has a mean length of 5 inches with a standard deviation of 0.60\mathbf{0 . 6 0}0.60 . -Find a 90%90 \%90% confidence interval for the population variance.

Find the critical value needed to test the null hypothesis that σ=40\sigma=40σ=40 against the alternative hypothesis that σ>\sigma>σ> 40 at α=0.01\alpha=0.01α=0.01 using a sample of size n=80n=80n=80 .

To find a 90%90 \%90% confidence interval for the standard deviation from a small sample, we use the values

The procedure used to evaluate the null hypothesis σ1=σ2\sigma_{1}=\sigma_{2}σ1​=σ2​ is the same as the procedure used to evaluate the null hypothesis σ=σ0\sigma=\sigma_{0}σ=σ0​ where σ0\sigma_{0}σ0​ is a constant.

A computed X2X^{2}X2 value that is larger than the Xα/22X_{\alpha / 2}^{2}Xα/22​ value allows us to reject the null hypothesis that __________ is based on a __________.

To test the hypothesis that two population standard deviations are equal, we use which of the following distributions?

A random sample of 11 copies of a particular mechanical component has a mean length of 5 inches with a standard deviation of 0.60\mathbf{0 . 6 0}0.60 . -Find a 95%95 \%95% confidence interval for the population standard deviation.

The FFF ratio can be used to evaluate the null hypothesis that the population standard deviation equals a given constant.

In testing for equality of two standard deviations using the $F$ statistic of $\alpha=0.02$ , the $F$ table value that must be exceeded to reject the null hypothesis is given by the symbol __________.

The hypothesis that two population standard deviations are equal can be rejected at the $10 \%$ level of significance if

The symbol $X^{2}$ has which of the following properties?

In order to test the hypothesis that a population $\sigma$ is a specified constant, it is never necessary to know the mean of the sample.

If $s_{1}^{2}=30$ and $s_{2}^{2}=20$ , then the $F$ ratio we use is __________.

An $F$ ratio is the ratio of two population standard deviations.

Finding a large-sample confidence interval for $\sigma$ requires the use of the normal distribution, whereas finding a small-sample confidence interval for $\sigma$ requires the use of $t$ distribution.

A random sample of 11 copies of a particular mechanical component has a mean length of 5 inches with a standard deviation of $\mathbf{0 . 6 0}$ . -Find a $90 \%$ confidence interval for the population variance.

Find the critical value needed to test the null hypothesis that $\sigma=40$ against the alternative hypothesis that $\sigma>$ 40 at $\alpha=0.01$ using a sample of size $n=80$ .

To find a $90 \%$ confidence interval for the standard deviation from a small sample, we use the values

The procedure used to evaluate the null hypothesis $\sigma_{1}=\sigma_{2}$ is the same as the procedure used to evaluate the null hypothesis $\sigma=\sigma_{0}$ where $\sigma_{0}$ is a constant.

A computed $X^{2}$ value that is larger than the $X_{\alpha / 2}^{2}$ value allows us to reject the null hypothesis that is based on a .

A random sample of 11 copies of a particular mechanical component has a mean length of 5 inches with a standard deviation of $\mathbf{0 . 6 0}$ . -Find a $95 \%$ confidence interval for the population standard deviation.

The $F$ ratio can be used to evaluate the null hypothesis that the population standard deviation equals a given constant.