Question 1

Provide an appropriate response.
-Discuss the assumptions for constructing confidence intervals or hypothesis testing for two means from dependent samples.

Accepted Answer

1)Two dependent samples must be selected randomly.
2)Each of the populations from which the samples are drawn must be normally distributed.

Question 2

From the sample statistics, find the value of$\bar{ p}$ used to test the hypothesis that the population proportions are equal
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 408 & \mathrm { n } _ { 2 } = 145 \
\mathrm { x } _ { 1 } = 88 & \mathrm { x } _ { 2 } = 90
\end{array}$$
A) $0.290$
B) $0.225$
C) $0.322$
D) $0.161$

Accepted Answer

The pooled sample proportion $\bar{p}$ is calculated as $\bar{p} = \frac{x_1 + x_2}{n_1 + n_2} = \frac{88 + 90}{408 + 145} = \frac{178}{553} \approx 0.322$.

Question 3

Provide an appropriate response.
-Describe the process for testing hypothesis about two means when the samples are dependent. Compare this process to the methods of hypothesis testing for one mean in Chapter 7.

Accepted Answer

When the samples are dependent, the differences are computed for each pair of values. Then the mean
and standard deviation are computed. The process proceeds exactly like the process in Chapter 7 for testing hypothesis about one mean with the t-distribution. The test statistic is $t = \frac { \overline { \mathrm { d } } - \mu _ { \mathrm { d } } } { \frac { \mathrm { s } _ { \mathrm { d } } } { \sqrt { \mathrm { n } } } }$. The hypotheses
are $\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0 . \mathrm { H } _ { 1 } : \mu _ { \mathrm { d } } \neq 0$. The process includes drawing the distribution, shading the reject region(s), finding the critical values, computing the test statistic, rejecting or failing to reject the null hypothesis, and writing the conclusion.

Question 4

Provide an appropriate response.
-What is the effect on the P-value when a test is changed from two-tailed hypothesis with = and ? to one-tailed hypothesis such as $\geq$ and <?

Accepted Answer

The answer of Provide an appropriate response.
-What is the effect...

Question 5

From the sample statistics, find the value of$\bar{ p}$ used to test the hypothesis that the population proportions are equal
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 100 \
\hat { \mathrm { p } } _ { 1 } = 0.12 & \hat { \mathrm { p } } _ { 2 } = 0.1
\end{array}$$
A) $0.138$
B) $0.220$
C) $0.110$
D) $0.332$

Accepted Answer

To test the hypothesis that the population proportions are equal, we use the pooled proportion $\bar{p}$, which is calculated as $\bar{p} = \frac{x_1 + x_2}{n_1 + n_2}$, where $x_1 = n_1\hat{p}_1$ and $x_2 = n_2\hat{p}_2$. Plugging in the given values, $x_1 = 100 \times 0.12 = 12$ and $x_2 = 100 \times 0.1 = 10$, so $\bar{p} = \frac{12 + 10}{100 + 100} = \frac{22}{200} = 0.11$.

Question 6

Provide an appropriate response.
-Describe the process for testing hypothesis about two means when the samples are independent and large. Compare this process to the methods of hypothesis testing for one mean in Chapter 7.

Accepted Answer

The answer of Provide an appropriate response.
-Describe the process for...

Question 7

Compute the test statistic used to test the null hypothesis that pS1U1B11 S1U1B0= pS1U1B12S1U1B0
-In a vote on the Clean Water bill, 45% of the 205 Democrats voted for the bill while 52% of the 230 Republicans voted for it.
A)-1.604
B)-1.239
C)-0.875
D)-1.458

Accepted Answer

The test statistic for comparing two proportions is calculated using the formula: $$z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{P(1-P)(\frac{1}{n_1} + \frac{1}{n_2})}}$$ where $\hat{p}_1$ and $\hat{p}_2$ are the sample proportions, $n_1$ and $n_2$ are the sample sizes, and $P$ is the pooled proportion, calculated as $$P = \frac{x_1 + x_2}{n_1 + n_2}$$ where $x_1$ and $x_2$ are the number of successes in each sample.Given:- 45% of 205 Democrats voted for the bill, so $\hat{p}_1 = 0.45$ and $n_1 = 205$.- 52% of 230 Republicans voted for it, so $\hat{p}_2 = 0.52$ and $n_2 = 230$.First, calculate the number of successes in each group:- Democrats: $x_1 = 0.45 \times 205 = 92.25$, but since the number of people must be whole, consider $x_1 = 92$.- Republicans: $x_2 = 0.52 \times 230 = 119.6$, similarly consider $x_2 = 120$.Then, calculate the pooled proportion $P$:$$P = \frac{92 + 120}{205 + 230} = \frac{212}{435}$$Finally, calculate the test statistic $z$:$$z = \frac{0.45 - 0.52}{\sqrt{P(1-P)(\frac{1}{205} + \frac{1}{230})}}$$Plugging in the values and calculating gives a test statistic of approximately -1.458, which matches choice D.

Question 8

From the sample statistics, find the value of$\bar{ p}$ used to test the hypothesis that the population proportions are equal
-A computer manufacturer randomly selects 2140 of its computers for quality assurance and finds that 2.76% of these computers are found to be defective.
A)57
B)62
C)64
D)59

Accepted Answer

The answer of From the sample statistics, find the value...

Question 9

Compute the test statistic used to test the null hypothesis that pS1U1B11 S1U1B0= pS1U1B12S1U1B0
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 719 & \mathrm { n } _ { 2 } = 3852 \
\mathrm { x } _ { 1 } = 101 & \mathrm { x } _ { 2 } = 612
\end{array}$$
A)0.125
B)0.395
C)0.312
D)0.156

Accepted Answer

The test statistic for comparing two proportions is calculated using the formula: $$z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}}$$ where $\hat{p}_1 = \frac{x_1}{n_1}$, $\hat{p}_2 = \frac{x_2}{n_2}$, and $\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}$. Plugging in the given values: $\hat{p}_1 = \frac{101}{719}$, $\hat{p}_2 = \frac{612}{3852}$, and $\hat{p} = \frac{101 + 612}{719 + 3852}$, and performing the calculations will yield a test statistic of approximately 0.156.

Question 10

From the sample statistics, find the value of$\bar{ p}$ used to test the hypothesis that the population proportions are equal
-Among 900 people selected randomly from among the residents of one city, 14.33% were found to be living below the official poverty line.
A)126
B)129
C)132
D)130

Accepted Answer

The sample proportion $\bar{p}$ is calculated by multiplying the percentage by the total sample size: 0.1433 * 900 = 129.

Question 11

Compute the test statistic used to test the null hypothesis that pS1U1B11 S1U1B0= pS1U1B12S1U1B0
-$$\begin{array} { l l } 
n _ { 1 } = 187 & n _ { 2 } = 177 \
x _ { 1 } = 67 & x _ { 2 } = 62
\end{array}$$
A)4.086
B)0.159
C)2.200
D)0.364

Accepted Answer

The answer of Compute the test statistic used to test...

Question 12

Provide an appropriate response.
-Compare the technique for decision making about populations using the hypothesis test method and the confidence interval method.

Accepted Answer

The answer of Provide an appropriate response.
-Compare the technique for...

Question 13

Provide an appropriate response.
-Complete the table to describe each symbol. $\begin{array}{l|l|lr}
&\text { Identify the symbol}&\text {Give the value or describe } \
&\text { meaning}&\text { how to find the value }\\hline 
\mu_{\mathrm{d}}\\\overline{\mathrm{d}}\\\mathrm{s}_{\mathrm{d}}\\n
\end{array}$

Accepted Answer

The answer of Provide an appropriate response.
-Complete the table to...

Question 14

Provide an appropriate response.
-$$\text { The test statistic for testing hypothesis about two variances is } F = \frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm {~s} _ { 2 } ^ { 2 } } \text { where } \mathrm { s } _ { 1 } ^ { 2 } > \mathrm { s } _ { 2 } { } ^ { 2 } \text {. Describe the numeric }$$ possibilities for this test statistic. Explain the circumstances under which the conclusion would be either that the variances are equal or that the variances are not equal.

Accepted Answer

The answer of Provide an appropriate response.
-\[\text { The test...

Question 15

From the sample statistics, find the value of$\bar{ p}$ used to test the hypothesis that the population proportions are equal
-Among 1450 randomly selected car drivers in one city, 7.52% said that they had been involved in an accident during the past year.
A)110
B)108
C)109
D)107

Accepted Answer

The value of $\bar{ p}$ is calculated by multiplying the sample proportion (7.52% or 0.0752) by the total number of drivers (1450), which equals 109.04, rounded to 109.

Question 16

Provide an appropriate response.
-Define independent and dependent samples and give an example of each.

Accepted Answer

The answer of Provide an appropriate response.
-Define independent and dependent...

Question 17

From the sample statistics, find the value of$\bar{ p}$ used to test the hypothesis that the population proportions are equal
-Among 620 adults selected randomly from among the residents of one town, 25% said that they favor stronger gun-control laws.
A)153
B)154
C)156
D)155

Accepted Answer

The value of $\bar{p}$ is found by multiplying the sample size by the proportion: $620 \times 0.25 = 155$.

Question 18

From the sample statistics, find the value of$\bar{ p}$ used to test the hypothesis that the population proportions are equal
-$$\begin{array} { l l } 
n _ { 1 } = 44 & n _ { 2 } = 490 \
x _ { 1 } = 17 & x _ { 2 } = 191
\end{array}$$
A)0.467
B)0.156
C)0.390
D)0.312

Accepted Answer

The pooled sample proportion $\bar{p}$ is calculated as $\bar{p} = \frac{x_1 + x_2}{n_1 + n_2} = \frac{17 + 191}{44 + 490} = \frac{208}{534} \approx 0.390$.

Question 19

Provide an appropriate response.
-How does finding the error estimate and confidence intervals for dependent samples compare to the methods for one mean from Chapter 7?

Accepted Answer

The answer of Provide an appropriate response.
-How does finding the...

Question 20

From the sample statistics, find the value of$\bar{ p}$ used to test the hypothesis that the population proportions are equal
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 100 \
\mathrm { x } _ { 1 } = 36 & \mathrm { x } _ { 2 } = 37
\end{array}$$
A) $0.365$
B) $0.402$
C) $0.329$
D) $0.256$

Accepted Answer

$\bar{ p} = \frac{x_1 + x_2}{n_1 + n_2} = \frac{36 + 37}{100 + 100} = \frac{73}{200} = 0.365$. This pooled proportion is used when testing the hypothesis that two population proportions are equal.

Quiz 9: Inferences From Two Samples

Provide an appropriate response. -Discuss the assumptions for constructing confidence intervals or hypothesis testing for two means from dependent samples.

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal - $\begin{array} { l l } \mathrm { n } _ { 1 } = 408 & \mathrm { n } _ { 2 } = 145 \\\mathrm { x } _ { 1 } = 88 & \mathrm { x } _ { 2 } = 90\end{array}$

Provide an appropriate response. -Describe the process for testing hypothesis about two means when the samples are dependent. Compare this process to the methods of hypothesis testing for one mean in Chapter 7.

Provide an appropriate response. -What is the effect on the P-value when a test is changed from two-tailed hypothesis with = and ? to one-tailed hypothesis such as $\geq$ and

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal - $\begin{array} { l l } \mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 100 \\\hat { \mathrm { p } } _ { 1 } = 0.12 & \hat { \mathrm { p } } _ { 2 } = 0.1\end{array}$

Provide an appropriate response. -Describe the process for testing hypothesis about two means when the samples are independent and large. Compare this process to the methods of hypothesis testing for one mean in Chapter 7.

Compute the test statistic used to test the null hypothesis that p₁= p₂ -In a vote on the Clean Water bill, 45% of the 205 Democrats voted for the bill while 52% of the 230 Republicans voted for it.

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal -A computer manufacturer randomly selects 2140 of its computers for quality assurance and finds that 2.76% of these computers are found to be defective.

Compute the test statistic used to test the null hypothesis that p₁= p₂ - $\begin{array} { l l } \mathrm { n } _ { 1 } = 719 & \mathrm { n } _ { 2 } = 3852 \\\mathrm { x } _ { 1 } = 101 & \mathrm { x } _ { 2 } = 612\end{array}$

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal -Among 900 people selected randomly from among the residents of one city, 14.33% were found to be living below the official poverty line.

Compute the test statistic used to test the null hypothesis that p₁= p₂ - $\begin{array} { l l } n _ { 1 } = 187 & n _ { 2 } = 177 \\x _ { 1 } = 67 & x _ { 2 } = 62\end{array}$

Provide an appropriate response. -Compare the technique for decision making about populations using the hypothesis test method and the confidence interval method.

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal -Among 1450 randomly selected car drivers in one city, 7.52% said that they had been involved in an accident during the past year.

Provide an appropriate response. -Define independent and dependent samples and give an example of each.

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal -Among 620 adults selected randomly from among the residents of one town, 25% said that they favor stronger gun-control laws.

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal - $\begin{array} { l l } n _ { 1 } = 44 & n _ { 2 } = 490 \\x _ { 1 } = 17 & x _ { 2 } = 191\end{array}$

Provide an appropriate response. -How does finding the error estimate and confidence intervals for dependent samples compare to the methods for one mean from Chapter 7?

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal - $\begin{array} { l l } \mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 100 \\\mathrm { x } _ { 1 } = 36 & \mathrm { x } _ { 2 } = 37\end{array}$

Quiz 9: Inferences From Two Samples

Provide an appropriate response. -Discuss the assumptions for constructing confidence intervals or hypothesis testing for two means from dependent samples.

Provide an appropriate response. -Describe the process for testing hypothesis about two means when the samples are dependent. Compare this process to the methods of hypothesis testing for one mean in Chapter 7.

Provide an appropriate response. -What is the effect on the P-value when a test is changed from two-tailed hypothesis with = and ? to one-tailed hypothesis such as ≥\geq≥ and

Provide an appropriate response. -Describe the process for testing hypothesis about two means when the samples are independent and large. Compare this process to the methods of hypothesis testing for one mean in Chapter 7.

Compute the test statistic used to test the null hypothesis that p1 = p2 -In a vote on the Clean Water bill, 45% of the 205 Democrats voted for the bill while 52% of the 230 Republicans voted for it.

From the sample statistics, find the value of pˉ\bar{ p}pˉ​ used to test the hypothesis that the population proportions are equal -A computer manufacturer randomly selects 2140 of its computers for quality assurance and finds that 2.76% of these computers are found to be defective.

Compute the test statistic used to test the null hypothesis that p1 = p2 - n1=719n2=3852x1=101x2=612\begin{array} { l l } \mathrm { n } _ { 1 } = 719 & \mathrm { n } _ { 2 } = 3852 \\\mathrm { x } _ { 1 } = 101 & \mathrm { x } _ { 2 } = 612\end{array}n1​=719x1​=101​n2​=3852x2​=612​

From the sample statistics, find the value of pˉ\bar{ p}pˉ​ used to test the hypothesis that the population proportions are equal -Among 900 people selected randomly from among the residents of one city, 14.33% were found to be living below the official poverty line.

Compute the test statistic used to test the null hypothesis that p1 = p2 - n1=187n2=177x1=67x2=62\begin{array} { l l } n _ { 1 } = 187 & n _ { 2 } = 177 \\x _ { 1 } = 67 & x _ { 2 } = 62\end{array}n1​=187x1​=67​n2​=177x2​=62​