Deck 9: Inferences From Two Samples

Question 1

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

Answer 1

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) $0.161$

Answer 2

$0.322$

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.

Answer 3

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

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

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) $0.332$

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.

Question 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.

A)-1.604
B)-1.239
C)-0.875
D)-1.458

Question 8

Find the number of successes x suggested by the given statement.
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

Question 9

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal

- $$\begin{array} { l l } \mathrm { n } _ { 1 } = 719 & \mathrm { n } _ { 2 } = 3852 \\\mathrm { x } _ { 1 } = 101 & \mathrm { x } _ { 2 } = 612\end{array}$$

A)0.125
B)0.395
C)0.312
D)0.156

Question 10

Find the number of successes x suggested by the given statement.
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

Question 11

Compute the test statistic used to test the null hypothesis that p₁ = p₂

- $$\begin{array} { l l } n _ { 1 } = 187 & n _ { 2 } = 177 \\x _ { 1 } = 67 & x _ { 2 } = 62\end{array}$$

A)4.086
B)0.159
C)2.200
D)0.364

Question 12

Provide an appropriate response.

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

Question 13

Provide an appropriate response.
Complete the table to describe each symbol.

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.

Question 15

Find the number of successes x suggested by the given statement.
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

Question 16

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

Question 17

Find the number of successes x suggested by the given statement.
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

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

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?

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) $0.256$

Question 21

Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected

-7 of 8,500 people vaccinated against a certain disease later developed the disease. 18 of 10,000 people vaccinated with a placebo later developed the disease. Test the claim that the vaccine is effective in lowering the incidence of the disease. Use a significance level of 0.02.

Question 22

Find the appropriate p-value to test the null hypothesis, H₀: p₁ = p₂, using a significance level of 0.05.

- $$\begin{array} { l l } n _ { 1 } = 50 & n _ { 2 } = 50 \\x _ { 1 } = 3 & x _ { 2 } = 7\end{array}$$

A).1201
B).0072
C).1836
D).0613

Question 23

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.

- $x _ { 1 } = 20 , n _ { 1 } = 43$ and $x _ { 2 } = 28 , n _ { 2 } = 60 ;$ Construct a $90 \%$ confidence interval for the difference between population proportions $\mathrm { P } 1 - \mathrm { P } 2$ .

A) $0.301 < \mathrm { p } _ { 1 } - \mathrm { P } _ { 2 } < 0.629$
B) $0.270 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.660$
C) $0.660 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.270$
D) $- 0.166 < p _ { 1 } - p _ { 2 } < 0.162$

Question 24

Use the traditional method to test the given hypothesis. 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. At the 0.05 significance level, test the claim that the recognition rates are the same in both states.

Question 25

Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected

-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. Test the claim that the proportion of smokers in the two age groups is the same. Use a significance level of 0.01.

Question 26

Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected

-In a random sample of 360 women, 65% favored stricter gun control laws. In a random sample of 220 men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of 0.05.

Question 27

Find the appropriate p-value to test the null hypothesis, H₀: p₁ = p₂, using a significance level of 0.05.

- $$\begin{array} { l l } \mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 140 \\\mathrm { x } _ { 1 } = 41 & \mathrm { x } _ { 2 } = 35\end{array}$$

A).0512
B).0086
C).0021
D).4211

Question 28

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

Question 29

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.

-x1=65,n1=90 and x2=79,n2=116,construct a 98% confidence interival for the difference berween
population proportions $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$ .

A) $- 0.084 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.848$
B) $- 0.108 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.190$
C) $0.596 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.848$
D) $0.572 < p _ { 1 } - p _ { 2 } < 0.872$

Question 30

Find the appropriate p-value to test the null hypothesis, H₀: p₁ = p₂, using a significance level of 0.05.

- $$\begin{array} { l l } n _ { 1 } = 100 & \mathrm { n } _ { 2 } = 100 \\\mathrm { x } _ { 1 } = 38 & \mathrm { x } _ { 2 } = 40\end{array}$$

A).2130
B).0412
C).7718
D).1610

Question 31

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.

-In a random sample of 300 women, $50 \%$ favored stricter gun control legislation. In a random sample of 200 men, $26 \%$ favored stricter gun control legislation. Construct a $98 \%$ confidence interval for the difference between the population proportions $\mathrm { p } 1$ - $\mathrm { p } 2$ .

A) $0.157 < \mathrm { p } 1 - \mathrm { p } _ { 2 } < 0.323$
B) $0.141 < \mathrm { p } 1 - \mathrm { p } 2 < 0.339$
C) $0.131 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.349$
D) $0.153 < p _ { 1 } - p _ { 2 } < 0.327$

Question 32

Compute the test statistic used to test the null hypothesis that p₁ = p₂

-Information about movie ticket sales was printed in a movie magazine. Out of fifty PG-rated movies, 45% had ticket sales in excess of $3,000,000. Out of thirty-five R-rated movies, 27% grossed over $3,000,000.

A)3.372
B)2.698
C)5.227
D)1.686

Question 33

Compute the test statistic used to test the null hypothesis that p₁ = p₂

-A random sampling of sixty pitchers from the National League and fifty-two pitchers from the American League showed that 16 National and 11 American League pitchers had E.R.A's below 3.5.

A)123.710
B)0.680
C)10.184
D)0.884

Question 34

Compute the test statistic used to test the null hypothesis that p₁ = p₂

-A report on the nightly news broadcast stated that 13 out of 111 households with pet dogs were burglarized and 23 out of 190 without pet dogs were burglarized.

A)0.000
B)-0.102
C)-0.041
D)-0.173

Question 35

Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected

-A researcher finds that of 1,000 people who said that they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1,200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are equal.

Question 36

Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected

-Use the given sample data to test the claim that p1 < p2. Use a significance level of 0.10. $$\begin{array} { l l l } \text { Sample } 1 & & \text { Sample } 2 \\\mathrm { n } _ { 1 } = 462 & & \mathrm { n } _ { 2 } = 380 \\\mathrm { x } _ { 1 } = 84 & & \mathrm { x } _ { 2 } = 95\end{array}$$

Question 37

Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected

- $$\begin{array}{l}\text { Use the given sample data to test the claim that } \mathrm { p } _ { 1 } > \mathrm { p } _ { 2 } \text {. Use a significance level of } 0.01 \text {. }\\\begin{array} { l l l } \text { Sample 1 } & \text { Sample 2 } \\\hline \mathrm { n } _ { 1 } = 85 & \mathrm { n } _ { 2 } = 90 \\\mathrm { x } _ { 1 } = 38 & \mathrm { x } _ { 2 } = 23\end{array}\end{array}$$

Question 38

Find the appropriate p-value to test the null hypothesis, H₀: p₁ = p₂, using a significance level of 0.05.

- $$\begin{array} { l l } n _ { 1 } = 50 & n _ { 2 } = 75 \\x _ { 1 } = 20 & x _ { 2 } = 15\end{array}$$

A).0001
B).0146
C).0032
D).1201

Question 39

Find the appropriate p-value to test the null hypothesis, H₀: p₁ = p₂, using a significance level of 0.05.

- $$\begin{array} { l l } \mathrm { n } _ { 1 } = 200 & \mathrm { n } _ { 2 } = 100 \\\mathrm { x } _ { 1 } = 11 & \mathrm { x } _ { 2 } = 8\end{array}$$

A).0201
B).1011
C).4010
D).0012

Question 40

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.

- $\mathrm { x } _ { 1 } = 27 , \mathrm { n } _ { 1 } = 67$ and $\mathrm { x } _ { 2 } = 27 , \mathrm { n } _ { 2 } = 72 ;$ Construct a $95 \%$ confidence interval for the difference between population proportions $\mathrm { P } 1 - \mathrm { P } 2$ .

A) $0.210 < \mathrm { p } 1 - \mathrm { p } 2 < 0.596$
B) $- 0.165 < \mathrm { p } 1 - \mathrm { p } 2 < 0.596$
C) $- 0.134 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.190$
D) $0.241 < \mathrm { p } 1 - \mathrm { p } 2 < 0.565$

Question 41

Test the indicated claim about the means of two populations. Assume that the two samples are independent and that they have been randomly selected.

-Two types of flares are tested for their burning times (in minutes)and sample results are given below. $$\begin{array} { l l l } \text { Brand } \mathrm { X }& { \text { Brand } \mathrm { Y } } \\\hline n=35 & \overline { \mathrm { n } } = 40 \\\overline { \mathrm { x } } = 19.4 & \overline { \mathrm { x } } = 15.1 \\\mathrm {~s} = 1.4 & \mathrm {~s} = 0.8\end{array}$$ Refer to the sample data to test the claim that the two populations have equal means. Use a 0.05 significance level.

Question 42

Use the computer display to solve the problem.

-When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.01 significance level, is there sufficient evidence to support the claim that the treatment group (variable 1)comes from a population with a mean that is greater than the mean for the placebo population? Explain. $$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \\\hline 2 & \text { Mean } & 171.6392 & 168.7718 \\\hline 3 & \text { Known Variance } & 47.51672 & 41.08293 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & \text { t } & 2.154057 & \\\hline 7 & \text { P(T>=t) one-tail } & 0.0158 & \\\hline 8 & \text { TCritical one-tail } & 1.644853 & \\\hline 9 & \text { P(T>=t) two-tail } & 0.0316 & \\\hline 10 & \text { tCritical two-tail } & 1.959961 & \\\hline\end{array}$$

Question 43

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected.

-Two types of flares are tested for their burning times (in minutes)and sample results are given below. $$\begin{array} { l l l } \text { Brand } X & & \text { Brand } Y \\\hline n =35& & \frac { n } { n } = 40 \\\bar { x } = 19.4 & & \bar { x } = 15.1 \\\mathrm {~s} = 1.4 & & \mathrm {~s} = 0.8\end{array}$$
Construct a $95 \%$ confidence interval for the differences $\mu _ { X } - \mu _ { Y }$ based on the sample data.

A) $3.6 < \mu _ { X } - \mu _ { Y } < 5.0$
B) $3.8 < \mu _ { X } - \mu Y < 4.8$
C) $3.5 < \mu X - \mu Y < 5.1$
D) $3.2 < \mu X - \mu Y < 5.4$

Question 44

Use the computer display to solve the problem.

-When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.05 significance level, is there sufficient evidence to support the claim that the treatment group (variable 1)comes from a population with a mean that is different from the mean for the placebo population? Explain. $$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \\\hline 2 & \text { Mean } & 65.10738 & 66.18251 \\\hline 3 & \text { Known Variance } & 8.102938 & 10.27387 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & \text { t } & - 1.773417 & \\\hline 7 & \text { P(T<=t) one-tail } & 0.0384 & \\\hline 8 & \text { TCritical one-tail } & 1.644853 & \\\hline 9 & \text { P(T<=t) two-tail } & 0.0768 & \\\hline 10 & \text { tCritical two-tail } & 1.959961 & \\\hline\end{array}$$

Question 45

Solve the problem.
To test the null hypothesis that the difference between two population proportions is equal to a nonzero constant c, use the test statistic

Question 46

Determine whether the samples are independent or consist of matched pairs.

-The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is cured for patients who use the medicine and another group of patients who use a placebo drug.

A)Matched pairs
B)Independent samples

Question 47

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected.

-Independent samples from two different populations yield the following data. $\overline { x _ { 1 } } = 383 , \overline { x _ { 2 } } = 448$ , s1 $= 44$ , s2 $= 18$ . The sample size is 177 for both samples. Find the 85 percent confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ .

A) $- 72 < \mu _ { 1 } - \mu _ { 2 } < - 58$
B) $- 66 < \mu _ { 1 } - \mu _ { 2 } < - 64$
C) $- 79 < \mu _ { 1 } - \mu _ { 2 } < - 51$
D) $- 71 < \mu _ { 1 } - \mu _ { 2 } < - 59$

Question 48

Determine whether the samples are independent or consist of matched pairs.

-The effect of caffeine as an ingredient is tested with a sample of regular soda and another sample with decaffeinated soda.

A)Matched pairs
B)Independent samples

Question 49

Use the computer display to solve the problem.

-When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.05 significance level, is there sufficient evidence to support the claim that the treatment group (variable 1)comes from a population with a mean that is less than the mean for the placebo population? Explain. $$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \\\hline 2 & \text { Mean } & 65.10738 & 66.18251 \\\hline 3 & \text { Known Variance } & 8.102938 & 10.27387 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & \text { t } & - 1.773417 & \\\hline 7 & \text { P(T<=t) one-tail } & 0.0384 & \\\hline 8 & \text { T Critical one-tail } & 1.644853 & \\\hline 9 & \text { P(T<=t) two-tail } & 0.0768 & \\\hline 10 & \text { tCritical two-tail } & 1.959961 & \\\hline\end{array}$$

Question 50

Use the computer display to solve the problem.

-When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.04 significance level, is there sufficient evidence to support the claim that the treatment group (variable 1)comes from a population with a mean that is different from the mean for the placebo population? Explain. $$\begin{array} { | l | l | l | l | } \hline & \text { t-Test: Two Sample for Means } & & \\\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \\\hline 2 & \text { Mean } & 171.6392 & 168.7718 \\\hline 3 & \text { Known Variance } & 47.51672 & 41.08293 \\\hline 4 & \text { Observations } & 50 & 50 \\\hline 5 & \text { Hypothesized Mean Difference } & 0 & \\\hline 6 & \text { t } & 2.154057 & \\\hline 7 & \text { P(T>=t) one-tail } & 0.0158 & \\\hline 8 & \text { TCritical one-tail } & 1.644853 & \\\hline 9 & \text { P(T>=t) two-tail } & 0.0316 & \\\hline 10 & \text { tCritical two-tail } & 1.959961 & \\\hline\end{array}$$

Question 51

Determine whether the following statement regarding the hypothesis test for two population proportions is true or false: However small the difference between two population proportions, for sufficiently large sample sizes, the null hypothesis of equal population proportions is likely to be rejected.

Question 52

Determine whether the samples are independent or consist of matched pairs.

-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)Matched pairs
B)Independent samples

Question 53

Determine whether the samples are independent or consist of matched pairs.

-The accuracy of verbal responses is tested in an experiment in which individuals report their heights and then are measured. The data consist of the reported height and measured height for each individual.

A)Independent samples
B)Matched pairs

Question 54

Test the indicated claim about the means of two populations. Assume that the two samples are independent and that they have been randomly selected.

-A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to test the claim that the treatment population mean µ1 is smaller than the control population mean µ2. Test the claim using a significance level of 0.01.
$\begin{array} { l } \text { Treatment Group }& \text { Control Group}\\\hline \mathrm{n}_{1}=85 &\mathrm{n}_{2}=75 \\\overline{\mathrm{x}_{1}}=189.1 & \overline{\mathrm{x}_{2}}=203.7 \\\mathrm{~s}_{1}=38.7 & \mathrm{~s}_{2}=39.2\end{array}$

Question 55

Solve the problem.

-A researcher wished to perform a hypothesis test to test the claim that the rate of defectives among the computers of two different manufacturers are the same. She selects two independent random samples and obtains the following sample data. Manufacturer
A: $\mathrm { n } _ { 1 } = 400$ , rate of defectives: $1.5 \%$ Manufacturer
B: $\mathrm { n } _ { 2 } = 200$ , rate of defectives: $3.5 \%$
Can the methods of this section be used to perform a hypothesis test to test for the equality of the two population proportions? Go through the steps of checking whether the conditions for the hypothesis test for two population proportions are satisfied. Show your calculations and state your conclusion.

Question 56

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected.

-A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a $99 \%$ confidence interval for $\mathrm { u } _ { 1 }$ - $\mathrm { u } _ { 2 }$ where $u _ { 1 }$ and $u _ { 2 }$ represent the mean for the treatment group and the control group respectively.
$\begin{array} { l } \text { Treatment Group }& \text { Control Group}\\\hline \mathrm{n}_{1}=85 &\mathrm{n}_{2}=75 \\\overline{\mathrm{x}_{1}}=189.1 & \overline{\mathrm{x}_{2}}=203.7 \\\mathrm{~s}_{1}=38.7 & \mathrm{~s}_{2}=39.2\end{array}$

A) $- 1.3 < \mu _ { 1 } - \mu _ { 2 } < 30.5$
B) $- 29.0 < \mu _ { 1 } - \mu _ { 2 } < - 0.2$
C) $- 26.7 < \mu _ { 1 } - \mu _ { 2 } < - 2.5$
D) $- 30.9 < \mu _ { 1 } - \mu _ { 2 } < 1.7$

Question 57

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.

-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. Construct a $95 \%$ confidence interval for the difference between the population proportions $\mathrm { p } _ { 1 } - \mathrm { p } 2$ .

A) $0.025 <$ p $_ { 1 } -$ p $_ { 2 } < 0.135$
B) $0.035 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.125$
C) $0.032 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.128$
D) $0.048 < p _ { 1 } - p _ { 2 } < 0.112$

Question 58

Solve the problem.

-A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure:
A: The hypothesis $\mu _ { 1 } = \mu _ { 2 }$ would be rejected at the $5 \%$ level of significance.
B: The hypothesis $\mu _ { 1 } = \mu _ { 2 }$ would be rejected at the $10 \%$ level of significance.
C: The hypothesis $\mu _ { 1 } = \mu _ { 2 }$ would be rejected at the $1 \%$ level of significance.

A) A, B, and C
B) A only
C) A and C
D) A and B

Question 59

Solve the problem.

-The sample size needed to estimate the difference between two population proportions to within a margin of error $\mathrm { E }$ with a confidence level of $1 - \alpha$ can be found as follows: in the expression
$$E = z _ { \alpha / 2} \sqrt { \frac { p _ { 1 } q _ { 1 } } { \mathrm { n } _ { 1 } } + \frac { \mathrm { p } _ { 2 } \mathrm { q } _ { 2 } } { \mathrm { n } _ { 2 } } }$$
replace $\mathrm { n } _ { 1 }$ and $\mathrm { n } _ { 2 }$ by $\mathrm { n }$ (assuming both samples have the same size) and replace each of $\mathrm { p } _ { 1 } , \mathrm { q } _ { 1 } , \mathrm { p } _ { 2 }$ , and $\mathrm { q } _ { 2 }$ by $0.5$ (because their values are not known). Then solve for $n$ .

Use this approach to find the size of each sample if you want to estimate the difference between the proportions . and women who plan to vote in the next presidential election. Assume that you want $99 \%$ confidence that your no more than $0.03$ .

A) 3017
B) 2135
C) 3685
D) 1432

Question 60

Solve the problem.
To test the null hypothesis that the difference between two population proportions is equal to a nonzero constant c, use the test statistic

Question 61

Find s_d.

-The differences between two sets of dependent data are -1, 5, -4, 2. Round to the nearest tenth.

A)2.0
B)3.9
C)89.7
D)3.1

Question 62

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { \mathrm { d } } = 0$ . Compute the value of the $t$ test statistic.

- $\begin{array}{l|ccccc}x & 30&38&25&26&28&27&33&35\\\hline y &28&34&34&26&29&32&33&34\end{array}$

A) $t = - 0.185$
B) $t = 0.690$
C) $t = - 1.480$
D) $t = - 0.523$

Question 63

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { \mathrm { d } } = 0$ . Compute the value of the $t$ test statistic.

-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? $$\begin{array} { r | r r r r r r r r r } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } & \text { I } \\\hline \text { Before } & 168 & 180 & 157 & 132 & 202 & 124 & 190 & 210 & 171 \\\hline \text { After } & 162 & 178 & 145 & 125 & 171 & 126 & 180 & 195 & 163\end{array}$$

A)0.351
B)1.052
C)3.156
D)9.468

Question 64

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

-We wish to compare the means of two populations using paired observations. Suppose that $\bar { d } = 3.125 , \mathrm {~S} _ { \mathrm { d } } =$ $2.911$ , and $\mathrm { n } = 8$ , and that you wish to test the following hypothesis at the 5 percent level of significance:
$$\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0 \text { against } \mathrm { H } _ { 1 } : \boldsymbol { \mu } _ { \mathrm { d } } > 0 \text {. }$$
What decision rule would you use?

A) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.895$ and less than $1.895$ .
B) Reject $\mathrm { H } _ { 0 }$ if test statistic is less than $1.895$ .
C) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $1.895$ .
D) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.895$ .

Question 65

Determine whether the samples are independent or consist of matched pairs.

-A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. Give an expression for the population standard deviation of the $\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right)$ values in terms of $\mathrm { s } _ { 1 } , \mathrm {~s} _ { 2 } , \mathrm { n } _ { 1 }$ , and $\mathrm { n } _ { 2 }$ .

A) $\sqrt{\frac{s_{1}^{2}}{n_{1}}-\frac{s_{2}^{2}}{n_{2}}}$

B) $\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}$

C) $\sqrt{\frac{\mathrm{s}_{1}^{2}}{\mathrm{n}_{1}^{2}}+\frac{\mathrm{s}_{2}^{2}}{\mathrm{n} \frac{2}{2}}}$

D) $\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}$

Question 66

Find s_d.

-The differences between two sets of dependent data are 3, 21, 3, 27, 15. Round to the nearest tenth.

A)10.7
B)8.6
C)21.4
D)13.9

Question 67

The two data sets are dependent. Find $\bar { d }$ to the nearest tenth.

- $$\begin{array} { l | l l l l l l l } \mathrm { X } & 227 & 189 & 220 & 182 & 246 & 277 & 302 \\\hline \mathrm { Y } & 217 & 154 & 195 & 153 & 227 & 246 & 284\end{array}$$

A)143.4
B)23.9
C)14.3
D)31.1

Question 68

Find s_d.

-The differences between two sets of dependent data are 0.11, 0.21, 0.15, 0.12, 0.14. Round to the nearest hundredth.

A)0.06
B)0.02
C)0.12
D)0.04

Question 69

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { \mathrm { d } } = 0$ . Compute the value of the $t$ test statistic.

- $\begin{array}{l|ccccc}x & 11 & 6 & 12 & 6 & 11 \\\hline y & 8 & 8 & 8 & 7 & 6\end{array}$

A) $t = 0.415$
B) $t = 0.578$
C) $t = 1.292$
D) $t = 2.890$

Question 70

The two data sets are dependent. Find $\bar { d }$ to the nearest tenth.

- $$\begin{array} { l | l l l l l } \mathrm { X } & 12.0 & 11.3 & 10.1 & 12.9 & 11.6 \\\hline \mathrm { Y } & 13.2 & 12.6 & 13.5 & 10.7 & 12.4\end{array}$$

A)-1.2
B)-1.1
C)-0.9
D)-0.5

Question 71

The two data sets are dependent. Find $\bar { d }$ to the nearest tenth.

- $$\begin{array} { c | c c c c c c } \mathrm { X } & 8.3 & 5.3 & 7.9 & 8.5 & 6.8 & 5.7 \\\hline \mathrm { Y } & 8.1 & 7.5 & 9.5 & 7.7 & 8.1 & 9.3\end{array}$$

A)-0.8
B)-1.3
C)-7.8
D)-1.7

Question 72

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 greater than 0 . Given a sample of $\mathrm { n } = 15$ and a significance level of $\alpha = 0.01$ , what criterion would be used for rejecting the null hypothesis?

A) Reject null hypothesis if test statistic $< 2.624$ .
B) Reject null hypothesis if test statistic $> 2.602$ .
C) Reject null hypothesis if test statistic $> 2.977$ or $< - 2.977$ .
D) Reject null hypothesis if test statistic $> 2.624$ .

Question 73

Find s_d.

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

A)13.1
B)16.2
C)15.3
D)15.7

Question 74

Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that
two dependent samples have been randomly selected from normally distributed populations.
Five students took a math test before and after tutoring. Their scores were as follows. Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores.

Question 75

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 d for a population of paired data, is different from 0. Given a sample of 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 $> 1.717$ .
B) Reject null hypothesis if test statistic $> 2.074$ or $< - 2.074$ .
C) Reject null hypothesis if test statistic $> 2.069$ or $< - 2.069$ .
D) Reject null hypothesis if test statistic $> 1.717$ or $< - 1.717$ .

Question 76

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { \mathrm { d } } = 0$ . Compute the value of the $t$ test statistic.

-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. $\begin{array} { l l l l l l l l l l l } \text { Plot: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\text { Before } & 9 & 9 & 8 & 7 & 6 & 8 & 5 & 9 & 10 & 11 \\ \text { After } & 10 & 9 & 9 & 8 & 7 & 10 & 6 & 10 & 10 & 12 \end{array}$
You wish to test the following hypothesis at the 5 percent level of significance.
$$\mathrm { H } _ { \mathrm { O } } : \mu _ { \mathrm { D } } = 0 \text { against } \mathrm { H } _ { 1 } : \mu _ { \mathrm { D } } \neq 0 \text {. }$$ What is the value of the appropriate test statistic?

A)2.536
B)1.584
C)5.014
D)2.033

Question 77

The two data sets are dependent. Find $\bar { d }$ to the nearest tenth.

- $$\begin{array} { l | l l l l l } \mathrm { A } & 56 & 59 & 55 & 63 & 51 \\\hline \mathrm { B } & 27 & 25 & 21 & 25 & 22\end{array}$$

A)41.0
B)32.8
C)19.7
D)42.6

Question 78

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. $\begin{array} { l l l l l l l l l l l } \text { Plot: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\hline \text { Before } & 9 & 9 & 8 & 7 & 6 & 8 & 5 & 9 & 10 & 11 \\ \text { After } & 10 & 9 & 9 & 8 & 7 & 10 & 6 & 10 & 10 & 12 \end{array}$
You wish the test the following hypothesis at the 1 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 $2.821$ .
B) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 2.821$ or less than $2.821$ .
C) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 2.821$ .
D) Reject $\mathrm { H } _ { 0 }$ if test statistic is less than $2.821$ .

Question 79

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { \mathrm { d } } = 0$ . Compute the value of the $t$ test statistic.

- $$\begin{array} { c | c c c c c c c c } \mathrm { x } & 7.1 & 5.9 & 3.4 & 10.3 & 4 & 10.2 & 9.3 & 7.1 \\\hline \mathrm { y } & 5.3 & 5.6 & 4.5 & 5.6 & 4.4 & 4.9 & 5.4 & 5.4\end{array}$$

A)t = 6.792
B)t = 0.998
C)t = 2.391
D)t = 0.845

Question 80

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. $\begin{array} { l l l l l l l l l l l } \text { Plot: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\hline \text { Before } & 9 & 9 & 8 & 7 & 6 & 8 & 5 & 9 & 10 & 11 \\ \text { After } & 10 & 9 & 9 & 8 & 7 & 10 & 6 & 10 & 10 & 12 \end{array}$
You wish to test the following hypothesis at the 1 percent level of significance.
$\mathrm { H } _ { 0 } : \mu _ { \mathrm { D } } = 0$ against $\mathrm { H } _ { 1 } : \mu _ { \mathrm { D } } \neq 0$
What decision rule would you use?

A) Reject $\mathrm { H } _ { 0 }$ if test statistic is less than $- 3.250$ .
B) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $3.250$ .
C) Reject $\mathrm { H } _ { 0 }$ if test statistic is less than $- 3.250$ or greater than $3.250$ .
D) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 3.250$ or less than $3.250$ .