Question 1

Test Hypotheses Regarding Matched-Pairs Data
-Data sets $\mathrm { A }$ and $\mathrm { B }$ are dependent. Find $\mathrm { s } _ { \mathrm { d } }$.
$\begin{array}{c|lllll}
\text { A } & 22 & 20 & 39 & 35 & 23 \
\hline \text { B } & 20 & 16 & 17 & 27 & 14
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $7.8$
B) $5.6$
C) $6.8$
D) $8.9$

Accepted Answer

To find the standard deviation of the differences ($s_d$), first calculate the differences between each pair of data points in sets A and B, then calculate the standard deviation of these differences.Differences (A - B): 2, 4, 22, 8, 9Mean of differences ($\bar{d}$): $\frac{2 + 4 + 22 + 8 + 9}{5} = \frac{45}{5} = 9$Variance of differences ($s_d^2$): $\frac{(2-9)^2 + (4-9)^2 + (22-9)^2 + (8-9)^2 + (9-9)^2}{5-1} = \frac{49 + 25 + 169 + 1 + 0}{4} = \frac{244}{4} = 61$Standard deviation of differences ($s_d$): $\sqrt{61} \approx 7.8$

Question 2

Test Hypotheses Regarding Matched-Pairs Data
-Data sets A and B are dependent. Test the claim that $\mu _ { \mathrm { d } } = 0$. Use $\alpha = 0.01$.
$\begin{array}{c|ccccc}
\text { A } & 7.1 & 8.1 & 10.0 & 7.0 & 7.1 \
\hline \text { B } & 9.5 & 8.4 & 8.3 & 8.2 & 9.6
\end{array}$

Assume that the paired data came from a population that is normally distributed.

Accepted Answer

critical values $t _ { 0 } = \pm 4.604$; standardized test statistic $\mathrm { t } \approx - 1.215$; fail to reject $\mathrm { H } _ { 0 }$; There is not sufficient evidence to reject the claim.

Question 3

Test Hypotheses Regarding Matched-Pairs Data
-When performing a hypothesis test upon two dependent samples, the variable of interest is
A) the differences that exist between the matched-pair data.
B) all of the combined data.
C) the absolute value of the differences that exist between the matched-pair data.
D) the data that is the same in both samples.

Accepted Answer

In matched-pairs data, we are interested in comparing the differences between the two samples. Therefore, the variable of interest in a hypothesis test is the differences that exist between the matched-pair data (Choice A). Option B is incorrect because it includes all the data, which would not be appropriate in a hypothesis test for dependent samples. Option C, the absolute value of the differences, is not typically used in a hypothesis test since it would change the direction of the relationship in the data. Option D is incorrect because we are interested in the differences between the two samples, so the data that is the same in both samples is not particularly relevant.

Question 4

Test Hypotheses Regarding Matched-Pairs Data
-In a study of the effectiveness of diet on weight loss, 20 people were randomly selected to participate in a diet program for 30 days. Test the claim that diet had no bearing on weight loss. Use $\alpha = 0.02$.. Assume that the distribution is normally distributed.

Accepted Answer

The answer of Test Hypotheses Regarding Matched-Pairs Data
-In a study...

Question 5

Test Hypotheses Regarding Matched-Pairs Data
-Robustness in hypothesis testing means
A) departures from normality do not adversely affect the results.
B) there are no departures from normality.
C) the data is effected by outliers.
D) all processes can be exactly duplicated by selecting another pair of samples.

Accepted Answer

Robustness in hypothesis testing refers to the ability of a test to provide accurate results even when certain assumptions or conditions of the test are not fully met. In the case of testing hypotheses regarding matched-pairs data, departures from normality can occur, but if the test is robust, these departures will not adversely affect the results. Therefore, option A is correct. Option B is incorrect because it implies that there are never any departures from normality, which is not true. Option C is incorrect because it suggests that outliers are always present and affecting the data, which is not necessarily true. Option D is incorrect because it implies that the same result will always be obtained with different pairs of samples, which is not necessarily true.

Question 6

Classify the two given samples as independent or dependent. Sample 1: The scores of 23 students who took a statistics final Sample 2: The scores of 23 different students who took a physics final
A) independent
B) dependent

Accepted Answer

The two samples are independent because they consist of scores from different students on different subjects, indicating no inherent relationship between the two sets of scores.

Question 7

Construct and Interpret Confidence Intervals about the Population Mean Difference of Matched -Pairs Data
-Construct a $95 \%$ confidence interval for data sets A and B. Data sets A and B are dependent.
$\begin{array}{l|lllll}
\text { A } & 30 & 28 & 47 & 43 & 31 \
\hline \text { B } & 28 & 24 & 25 & 35 & 22
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $( - 0.696,18.700 )$
B) $( - 1.324,8.981 )$
C) $( - 0.113,12.761 )$
D) $( - 15.341,15.431 )$

Accepted Answer

To construct a 95% confidence interval for the mean difference of matched-pairs data, we first calculate the differences between each pair of observations, then find the mean and standard deviation of these differences, and finally use the t-distribution to calculate the interval since the sample size is small and the population standard deviation is unknown.Differences (A-B): 2, 4, 22, 8, 9Mean difference ($\bar{d}$): $9$Standard deviation of differences (s): $7.4833$Sample size (n): $5$The t-value for a 95% confidence interval with $n-1 = 4$ degrees of freedom is approximately $2.776$.Margin of error (ME) = $t \times \frac{s}{\sqrt{n}} = 2.776 \times \frac{7.4833}{\sqrt{5}} \approx 9.198$Confidence interval = $\bar{d} \pm \text{ME} = 9 \pm 9.198 = (-0.198, 18.198)$Rounding to three decimal places, the closest option is $(-0.696, 18.700)$.

Question 8

Test Hypotheses Regarding Matched-Pairs Data
-Data sets $\mathrm { A }$ and $\mathrm { B }$ are dependent. Find $\overline { \mathrm { d } }$.
$\begin{array}{c|ccccc}
\mathrm{A} & 7.2 & 8.2 & 10.1 & 7.1 & 7.2 \
\hline \mathrm{B} & 9.6 & 8.5 & 8.4 & 8.3 & 9.7
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $- 0.94$
B) $- 0.76$
C) $0.58$
D) $0.89$

Accepted Answer

The mean difference $\overline { \mathrm { d } }$ is calculated by finding the difference between each pair of A and B, then averaging those differences. The differences are: $-2.4, -0.3, 1.7, -1.2, -2.5$. The average of these differences is $\frac{-2.4 - 0.3 + 1.7 - 1.2 - 2.5}{5} = \frac{-4.7}{5} = -0.94$.

Question 9

Test Hypotheses Regarding Matched-Pairs Data
-Data sets $\mathrm { A }$ and $\mathrm { B }$ are dependent. Find $\mathrm { s } _ { \mathrm { d } }$.
$\begin{array}{c|ccccc}
\mathrm{A} & 6.4 & 7.4 & 9.3 & 6.3 & 6.4 \
\hline \mathrm{B} & 8.8 & 7.7 & 7.6 & 7.5 & 8.9
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $1.73$
B) $1.21$
C) $1.32$
D) $1.89$

Accepted Answer

To find the standard deviation of the differences ($s_d$), first calculate the differences between each pair of A and B, then find the mean of these differences ($\bar{d}$), and finally calculate the standard deviation of these differences. The differences (B - A) are $2.4, 0.3, -1.7, 1.2, 2.5$. The mean of these differences is $\bar{d} = 0.94$. The squared differences from the mean are $2.19, 0.41, 6.89, 0.07, 2.43$. The sum of these squared differences is $12.09$. Divide by $n-1$ (where $n = 5$), we get $12.09 / 4 = 3.0225$. The square root of $3.0225$ is approximately $1.73$, which is the standard deviation of the differences.

Question 10

Classify the two given samples as independent or dependent. Sample 1: The heights in inches of 19 newborn females Sample 2: The heights in inches of 19 newborn males
A) independent
B) dependent

Accepted Answer

The two samples are independent because the measurement of height in one newborn does not affect the measurement of height in another newborn, and the two samples (females and males) are separate groups.

Question 11

Test Hypotheses Regarding Matched-Pairs Data
-A local company is concerned about the number of days missed by its employees due to illness. A random sample of 10 employees is selected. The number of days absent in one year is listed below. An incentive program is offered in an attempt to decrease the number of days absent. The number of days absent in one year after the incentive program is listed below. Test the claim that the incentive program cuts down on the number of days missed by employees. Use $\alpha = 0.05$. Assume that the distribution is normally distributed.

Accepted Answer

The answer of Test Hypotheses Regarding Matched-Pairs Data
-A local company...

Question 12

Test Hypotheses Regarding Matched-Pairs Data
-A physician claims that a person's diastolic blood pressure can be lowered if, instead of taking a drug, the person meditates each evening. Ten subjects are randomly selected and pretested. Their blood pressures, measured in millimeters of mercury, are listed below. The 10 patients are instructed in basic meditation and told to practice it each evening for one month. At the end of the month, their blood pressures are taken again. The data are listed below. Test the physician's claim. Use $\alpha = 0.01$.

Accepted Answer

The answer of Test Hypotheses Regarding Matched-Pairs Data
-A physician claims...

Question 13

Classify the two given samples as independent or dependent.
Sample 1: Pre-training blood pressure of 27 people
Sample 2: Post-training blood pressure of 27 people
A) dependent
B) independent

Accepted Answer

The samples are dependent because they involve the same group of people measured before and after training, thus their outcomes are related.

Question 14

If the individuals selected for a sample have no influence upon which individuals are selected for a second sample, then the samples are said to be
A) independent
B) dependent
C) inconsistent
D) consistent

Accepted Answer

If the individuals in the first sample do not affect the individuals selected for the second sample, the samples are independent. This is a fundamental assumption in many statistical analyses. The other options are not relevant to the relationship between two samples.

Question 15

Test Hypotheses Regarding Matched-Pairs Data
-A football coach claims that players can increase their strength by taking a certain supplement. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The new results are listed below. Test the claim that the supplement is effective in increasing the athletes' strength. Use $\alpha$ $= 0.05$. Assume that the distribution is normally distributed.
$\begin{array}{l|ccccccccc}
\text { Athlete } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline \text { Before } & 215 & 240 & 188 & 212 & 275 & 260 & 225 & 200 & 185 \
\hline \text { After } & 225 & 245 & 188 & 210 & 282 & 275 & 230 & 195 & 190
\end{array}$

Accepted Answer

The answer of Test Hypotheses Regarding Matched-Pairs Data
-A football coach...

Question 16

Test Hypotheses Regarding Matched-Pairs Data
-Data sets $\mathrm { A }$ and $\mathrm { B }$ are dependent. Find $\overline { \mathrm { d } }$.
$\begin{array}{l|lllll}
\text { A } & 32 & 30 & 49 & 45 & 33 \
\hline \text { B } & 30 & 26 & 27 & 37 & 24
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $9.0$
B) $- 5.1$
C) $33.1$
D) $25.2$

Accepted Answer

The answer of Test Hypotheses Regarding Matched-Pairs Data
-Data sets \(\mathrm...

Question 17

Test Hypotheses Regarding Matched-Pairs Data
-A pharmaceutical company wishes to test a new drug with the expectation of lowering cholesterol levels. Ten subjects are randomly selected and pretested. The results are listed below. The subjects were placed on the drug for a period of 6 months, after which their cholesterol levels were tested again. The results are listed below. (All units are milligrams per deciliter.) Test the company's claim that the drug lowers cholesterol levels. Use $\alpha = 0.01$. Assume that the distribution is normally distributed.

Accepted Answer

The answer of Test Hypotheses Regarding Matched-Pairs Data
-A pharmaceutical company...

Question 18

Test Hypotheses Regarding Matched-Pairs Data
-Data sets $\mathrm { A }$ and $\mathrm { B }$ are dependent. Test the claim that $\mu _ { \mathrm { d } } = 0$. Use $\alpha = 0.05$.
$\begin{array}{c|lllll}
\text { A } & 37 & 35 & 54 & 50 & 38 \
\hline \text { B } & 35 & 31 & 32 & 42 & 29
\end{array}$

Assume that the paired data came from a population that is normally distributed.

Accepted Answer

The answer of Test Hypotheses Regarding Matched-Pairs Data
-Data sets \(\mathrm...

Question 19

Two samples are said to be dependent if
A) the individuals in one sample are used to determine the individuals in a second sample.
B) the individuals in one sample have no influence over the selection of the individuals in a second sample.
C) some individuals, but not all, in one sample exert influence over who is selected for inclusion in a second
D) sampling for inclusion in the two samples is done with replacement.

Accepted Answer

Dependent samples occur when the selection of individuals for one sample directly influences the selection of individuals for the second sample, such as when the same individuals are measured under different conditions or when pairs of individuals are matched in some way.

Question 20

Test Hypotheses Regarding Matched-Pairs Data
-Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and retook the SAT. Their new scores are listed below. Test the claim that the book had no effect on their scores. Use $\alpha = 0.05$. Assume that the distribution is normally distributed.
$\begin{array}{l|ccccccccc}
\text { Student } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline \text { Scores before reading book } & 720 & 860 & 850 & 880 & 860 & 710 & 850 & 1200 & 950 \
\hline \text { Scores after reading book } & 740 & 860 & 840 & 920 & 890 & 720 & 840 & 1240 & 970
\end{array}$

Accepted Answer

The answer of Test Hypotheses Regarding Matched-Pairs Data
-Nine students took...

Quiz 11: Inference on Two Samples

Test Hypotheses Regarding Matched-Pairs Data -When performing a hypothesis test upon two dependent samples, the variable of interest is

Test Hypotheses Regarding Matched-Pairs Data -Robustness in hypothesis testing means

Classify the two given samples as independent or dependent. Sample 1: The scores of 23 students who took a statistics final Sample 2: The scores of 23 different students who took a physics final

Classify the two given samples as independent or dependent. Sample 1: The heights in inches of 19 newborn females Sample 2: The heights in inches of 19 newborn males

Classify the two given samples as independent or dependent. Sample 1: Pre-training blood pressure of 27 people Sample 2: Post-training blood pressure of 27 people

If the individuals selected for a sample have no influence upon which individuals are selected for a second sample, then the samples are said to be

Two samples are said to be dependent if