Question 1

Consider the set of differences between two dependent sets: 84, 85, 83, 63, 61, 100, 98. Round to the nearest tenth.
A) 16.2
B) 15.3
C) 15.7
D) 13.1

Accepted Answer

The standard deviation of the set of differences is calculated and rounded to the nearest tenth, resulting in 15.3.

Question 2

Find the number of successes x suggested by the given statement.
-A computer manufacturer randomly selects 2880 of its computers for quality assurance and finds that 2.43% of these computers are found to be defective.
A) 73
B) 75
C) 70
D) 68

Accepted Answer

The answer of Find the number of successes x suggested...

Question 3

State what the given confidence interval suggests about the two population means.
-A researcher was interested in comparing the heights of women in two different countries. Independent simple random samples of 9 women from country A and 9 women from country B yielded the following heights (in inches).

$\begin{array}{c|c}
\text { Country A } & \text { Country B } \
\hline 65.3 & 64.1 \
60.2 & 66.4 \
61.7 & 61.7 \
65.8 & 62.0 \
61.0 & 67.3 \
64.6 & 64.9 \
60.0 & 64.7 \
65.4 & 68.0 \
59.0 & 63.6
\end{array}$

The following $90 \%$ confidence interval was obtained for $\mu _ { 1 } - \mu _ { 2 }$, the difference between the mean height of women in country A and the mean height of women in country B. $- 4.34$ in. $< \mu _ { 1 } - \mu _ { 2 } < - 0.03$ in What does the confidence interval suggest about the population means?

A) The confidence interval includes 0 which suggests that the two population means might be equal. There doesn't appear to be a significant difference between the mean height of women from country A and the mean height of women from country B.
B) The confidence interval includes only negative values which suggests that the mean height of women from country A is greater than the mean height of women from country B.
C) The confidence interval includes only negative values which suggests that the mean height of women from country A is smaller than the mean height of women from country B.
D) The confidence interval includes only negative values which suggests that the two population means might be equal. There doesn't appear to be a significant difference between the mean height of women from country A and the mean height of women from country B.

Accepted Answer

The confidence interval includes only negative values, which suggests that the mean height of women from country A is smaller than the mean height of women from country B.

Question 4

Find the number of successes x suggested by the given statement.
-Among 1430 randomly selected car drivers in one city, 7.2% said that they had been involved in an accident during the past year.
A) 101
B) 102
C) 104
D) 103

Accepted Answer

The answer of Find the number of successes x suggested...

Question 5

Construct the indicated confidence interval for the difference between population proportions $p _ { 1 } - p _ { 2 }$ . Assume that the samples are independent and that they have been randomly selected.
-$\mathrm { x } _ { 1 } = 68 , \mathrm { n } _ { 1 } = 93$ and $\mathrm { x } _ { 2 } = 78 , \mathrm { n } _ { 2 } = 111 ;$ Construct a $98 \%$ confidence interval for the difference between population proportions $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$.
A) $- 0.119 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.176$
B) $0.584 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.879$
C) $- 0.095 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.855$
D) $0.607 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.855$

Accepted Answer

The confidence interval for the difference between population proportions is calculated using the formula for the standard error of the difference between two proportions and the z-score for a 98% confidence level. The correct interval is $-0.119 < p_1 - p_2 < 0.176$.

Question 6

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis.
-A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The results are shown below. 
$\begin{array}{lcccccccccc}
\text { Plot: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \
\hline \text { Before } & 9 & 9 & 8 & 7 & 6 & 8 & 5 & 9 & 10 & 11 \
\text { After } & 10 & 9 & 9 & 8 & 7 & 10 & 6 & 10 & 10 & 12\\hline
\end{array}$
You wish the test the following hypothesis at the 10 percent level of significance.
$\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0$ against $\mathrm { H } _ { 1 } : \mu _ { \mathrm { d } } > 0$.
What decision rule would you use?
A) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than 1.383.
B) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.383$.
C) Reject $\mathrm { H } _ { 0 }$ if test statistic is less than 1.383.
D) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.383$ or less than $1.383$.

Accepted Answer

The test is right-tailed, so the critical value is found in the upper tail of the distribution. The critical value for a 10% level of significance is 1.383.

Question 7

Find sS1U1B1dS1U1B0
-The differences between two sets of dependent data are $- 2,2 , - 2,2$ . Round to the nearest tenth.
A) 1.2
B) 2.3
C) 1.8
D) 52.9

Accepted Answer

The answer of Find sS1U1B1dS1U1B0
-The differences between two sets of...

Question 8

The table shows the number of smokers in a random sample of 500 adults aged $20 - 24$ and the number of smokers in a random sample of 450 adults aged 25-29. Assume that you plan to use a significance level of $\alpha = 0.10$ to test the claim that $\mathrm { p } _ { 1 } \neq \mathrm { p } _ { 2 }$. Find the critical value(s) for this hypothesis test. Do the data provide sufficient evidence that the proportion of smokers in the 20-24 age group is different from the proportion of smokers in the 25-29 age group?
$\begin{array}{lcc}
\hline & \text { Age 20-24 } & \text { Age 25-29 } \
\hline \text { Number in sample } & 500 & 450 \
\text { Number of smokers } & 110 & 63 \
\hline
\end{array}$
A) $\mathrm { z } = \pm 1.28$; yes
B) $z = \pm 1.645$; yes
C) $\mathrm { z } = 1.28$; no
D) $z = \pm 1.96$; no

Accepted Answer

The critical value for a two-tailed test at $\alpha = 0.10$ is $z = \pm 1.645$. The test statistic calculated from the data would need to be compared to these critical values to determine if there is sufficient evidence to reject the null hypothesis.

Question 9

Assume that you plan to use a significance level of $\alpha = 0.05 \text { to test the claim that } \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ , Use the given sample sizes and
numbers of successes to find the P-value for the hypothesis test.
-$$\begin{array} { l l } 
n _ { 1 } = 100 & n _ { 2 } = 100 \
x _ { 1 } = 38 & x _ { 2 } = 40
\end{array}$$
A) 0.7718
B) 0.0412
C) 0.1610
D) 0.2130

Accepted Answer

The answer of Assume that you plan to use a...

Question 10

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is µd = 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed.
-The following table shows the weights of nine subjects before and after following a particular diet for two months. You wish to test the claim that the diet is effective in helping people lose weight.
What is the value of the appropriate test statistic? $$\begin{array} { r | c c c c c c c c c } 
\text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } & \text { I } \
\hline \text { Before } & 168 & 180 & 157 & 132 & 202 & 124 & 190 & 210 & 171 \
\hline \text { After } & 162 & 178 & 145 & 125 & 171 & 126 & 180 & 195 & 163
\end{array}$$
A) 1.052
B) 9.468
C) 0.351
D) 3.156

Accepted Answer

The test statistic is calculated using the differences between the before and after weights, finding the mean and standard deviation of these differences, and then using the formula for the t-test for paired samples. The correct calculation results in a t-value of approximately 3.156.

Question 11

Assume that you want to test the claim that the paired sample data come from a population for which the mean differencenis $\mu _ { \mathrm { d } } = 0$ 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed.
-$\begin{array}{c|ccccc}
\mathrm{x} & 9 & 1 & 7 & 7 & 11 \
\hline \mathrm{y} & 6 & 3 & 3 & 8 & 6
\end{array}$
A) $t = 1.292$
B) $t = 2.890$
C) $t = 0.415$
D) $\mathrm { t } = 0.578$

Accepted Answer

The correct answer is A because the t-test statistic is calculated as (x̄ - μd) / (sd / √n), where x̄ is the sample mean difference, μd is the hypothesized population mean difference, sd is the sample standard deviation of the differences, and n is the sample size. Plugging in the given values, we get t = (6 - 0) / (2.828 / √5) = 1.292.

Question 12

In a random sample of 500 people aged $20 - 24,22 \%$ were smokers. In a random sample of 450 people aged 25-29, 14\% were smokers. A $95 \%$ confidence interval for the difference between the proportion of 20-24 year olds and the proportion of 25-29 year olds who are smokers is $0.032 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.128$
Which of the following statements give a correct interpretation of this confidence interval?
I. We can be $95 \%$ confident that the interval $0.032$ to $0.128$ contains the true difference between the two population proportions.
II. There is a $95 \%$ chance that the true difference between the two population proportions lies between $0.032$ and $0.128$.
III. If the process were repeated many times, each time selecting random samples of 500 people aged 20-24 and 450 people aged 25-29 and each time constructing a confidence interval for $\mathrm { p } _ { 1 }$ $p _ { 2 } , 95 \%$ of the time the true difference between the two population proportions will lie between $0.032$ and $0.128$.
IV. If the process were repeated many times, each time selecting random samples of 500 people aged 20-24 and 450 people aged 25-29 and each time constructing a confidence interval for $p _ { 1 } -$ $\mathrm { p } _ { 2 } , 95 \%$ of the time the confidence interval limits will contain the true difference between the two population proportions.
A) I and IV
B) II and IV
C) I and III
D) II and III

Accepted Answer

Statement I correctly interprets the confidence interval as containing the true difference with 95% confidence. Statement IV correctly describes the frequentist interpretation of confidence intervals, where 95% of such intervals will contain the true difference if the process is repeated many times.

Question 13

The two data sets are dependent. Find $\overline { \mathrm { d } }$ to the nearest tenth.
-$$\begin{array} { l | l l l l l } 
\mathrm { X } & 12.7 & 11.3 & 12.9 & 12.9 & 13.0 \
\hline \mathrm { Y } & 11.5 & 12.6 & 11.1 & 10.7 & 10.5
\end{array}$$
A) 1.3
B) 0.8
C) 1.7
D) 1.6

Accepted Answer

The answer of The two data sets are dependent. Find...

Question 14

Assume that you plan to use a significance level of ? = 0.05 to test the claim that p $p _ { 1 } = p _ { 2 }$ , Use the given sample sizes and numbers of successes to find the P-value for the hypothesis test.
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 140 \
\mathrm { x } _ { 1 } = 41 & \mathrm { x } _ { 2 } = 35
\end{array}$$
A) 0.0021
B) 0.4211
C) 0.0086
D) 0.0512

Accepted Answer

The answer of Assume that you plan to use a...

Question 15

Determine whether the samples are independent or dependent.
-The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and after drug treatment. The data consist of before and after intensities for each patient.
A) Independent samples
B) Dependent samples

Accepted Answer

The samples are dependent because the before and after measurements are taken from the same patients, linking the two sets of data.

Question 16

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.
-A researcher was interested in comparing the resting pulse rates of people who exercise regularly and the pulse rates of people who do not exercise regularly. She obtained independent simple random samples of 16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse rates (in beats per minute) were recorded and the summary statistics
Are as follows.
 $\begin{array}{c|l}
\text { Do not exercise regularly } & \text { Exercise regularly } \
\hline \overline{\mathrm{x}}_{1}=72.3 \text { beats } / \mathrm{min} & \overline{\mathrm{x}}_{2}=68.2 \text { beats } / \mathrm{min} \
\mathrm{s}_{1}=10.9 \text { beats } / \mathrm{min} & \mathrm{s}_{2}=8.2 \text { beats } / \mathrm{min} \
\mathrm{n}_{1}=16 & \mathrm{n}_{2}=12
\end{array}$
Construct a 95\% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$, the difference between the mean pulse rate of people who do not exercise regularly and the mean pulse rate of people who exercise regularly.
A) $- 3.32$ beats $/ \mathrm { min } < \mu _ { 1 } - \mu _ { 2 } < 11.52$ beats $/ \mathrm { min }$
B) $- 3.34$ beats $/ \mathrm { min } < \mu _ { 1 } - \mu _ { 2 } < 11.54$ beats $/ \mathrm { min }$
C) $- 3.63$ beats $/ \mathrm { min } < \mu _ { 1 } - \mu _ { 2 } < 11.83$ beats $/ \mathrm { min }$
D) $- 3.65$ beats $/ \mathrm { min } < \mu _ { 1 } - \mu _ { 2 } < 11.85$ beats $/ \mathrm { min }$

Accepted Answer

The correct answer is A because the confidence interval is calculated as:$\left(\overline{\mathrm{x}}_{1}-\overline{\mathrm{x}}_{2}\right) \pm t_{\alpha/2} \sqrt{\frac{\mathrm{s}_{1}^{2}}{\mathrm{n}_{1}}+\frac{\mathrm{s}_{2}^{2}}{\mathrm{n}_{2}}}$where $t_{\alpha/2}$ is the critical value from the t-distribution with $\nu$ degrees of freedom, where $\nu$ is the smaller of $\mathrm{n}_{1}-1$ and $\mathrm{n}_{2}-1$.In this case, $\nu$ is the smaller of 15 and 11, which is 11. The critical value from the t-distribution with 11 degrees of freedom and a significance level of 0.05 is 2.201.Plugging in the values, we get:$(72.3-68.2) \pm 2.201 \sqrt{\frac{10.9^{2}}{16}+\frac{8.2^{2}}{12}}$which simplifies to:$-4.1 \pm 7.4$or$-3.32$ beats $/ \mathrm { min } < \mu _ { 1 } - \mu _ { 2 } < 11.52$ beats $/ \mathrm { min }$

Question 17

Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed.
-The table below shows the weights of 9 subjects before and after following a particular diet for two months. $\begin{array}{r|ccccccccc}
\text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } & \text { I } \
\hline \text { Before } & 168 & 180 & 157 & 132 & 202 & 124 & 190 & 210 & 171 \
\hline \text { After } & 162 & 178 & 145 & 125 & 171 & 126 & 180 & 195 & 163
\end{array}$
Construct a $99 \%$ confidence interval for the mean difference of the "before" minus "after" weights.
A) $- 0.6 < \mu _ { \mathrm { d } } < 20.4$
B) $2.4 < \mu _ { \text {d } } < 17.4$
C) $2.8 < \mu _ { \mathrm { d } } < 17.0$
D) $4.51 < \mu _ { \mathrm { d } } < 15.7$

Accepted Answer

The answer of Construct a confidence interval for µd, the...

Question 18

Construct the indicated confidence interval for the difference between population proportions p1 - p2. Assume that the samples are independent and that they have been randomly selected.
-A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval for the difference between the two population proportions.

A) $- 0.0443 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0976$
B) $- 0.0034 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0566$
C) $0.0247 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0286$
D) $- 0.0177 < p _ { 1 } - p _ { 2 } < 0.1243$

Accepted Answer

The correct answer is A because the confidence interval is calculated as:p1 - p2 +/- z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and z is the z-score corresponding to the desired confidence level.In this case, we have:p1 = 193 / 558 = 0.346p2 = 196 / 614 = 0.319n1 = 558n2 = 614z = 2.576 (for a 99% confidence level)Plugging these values into the formula, we get:0.346 - 0.319 +/- 2.576 * sqrt((0.346 * (1 - 0.346) / 558) + (0.319 * (1 - 0.319) / 614))= 0.027 +/- 0.071= (-0.0443, 0.0976)

Question 19

Assume that you plan to use a significance level of $\alpha = 0.05 \text { to test the claim that } \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ se the given sample sizes and
numbers of successes to find the z test statistic for the hypothesis test.
-A random sampling of sixty pitchers from the National League and fifty-two pitchers from the American League showed that 15 National and 10 American League pitchers had E.R.A's below 3.5. 
A) $z = 127.077$
B) $\mathrm { z } = 10.583$
C) $z = 0.731$
D) $z = 0.950$

Accepted Answer

The z test statistic is calculated using the formula for the difference between two proportions. The calculated z value is approximately 0.731.

Question 20

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. -Suppose you wish to test the claim that $\mu _ { \mathrm { d } }$, the mean value of the differences $\mathrm { d }$ for a population of paired data, is different from 0 . Given a sample of $\mathrm { n } = 23$ and a significance level of $\alpha = 0.05$, what criterion would be used for rejecting the null hypothesis? A) Reject null hypothesis if test statistic $> 2.074$ or $< - 2.074$. B) Reject null hypothesis if test statistic $> 2.069$ or $< - 2.069$. C) Reject null hypothesis if test statistic $> 1.717$ or $< - 1.717$. D) Reject null hypothesis if test statistic $> 1.717$.

Accepted Answer

The answer of Determine the decision criterion for rejecting the...

Quiz 9: Inferences From Two Samples

Consider the set of differences between two dependent sets: 84, 85, 83, 63, 61, 100, 98. Round to the nearest tenth.

Find the number of successes x suggested by the given statement. -A computer manufacturer randomly selects 2880 of its computers for quality assurance and finds that 2.43% of these computers are found to be defective.

Find the number of successes x suggested by the given statement. -Among 1430 randomly selected car drivers in one city, 7.2% said that they had been involved in an accident during the past year.

Find s_d -The differences between two sets of dependent data are $- 2,2 , - 2,2$ . Round to the nearest tenth.

The two data sets are dependent. Find $\overline { \mathrm { d } }$ to the nearest tenth. - $\begin{array} { l | l l l l l } \mathrm { X } & 12.7 & 11.3 & 12.9 & 12.9 & 13.0 \\\hline \mathrm { Y } & 11.5 & 12.6 & 11.1 & 10.7 & 10.5\end{array}$

Determine whether the samples are independent or dependent. -The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and after drug treatment. The data consist of before and after intensities for each patient.