A consumer advice web site tested a fuel additive. The distance that 12 cars could travel on five gallons of gasoline was recorded without and then with the additive. The results were as follow. $\begin{array}{l|cccccccccccc} \text { Car } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \text { No Additive } & 176 & 145 & 124 & 179 & 139 & 186 & 180 & 176 & 90 & 159 & 92 & 167 \\ \text { With additive } & 186 & 162 & 130 & 179 & 149 & 191 & 193 & 184 & 105 & 159 & 94 & 173 \end{array}$ a) Compute the test statistic b) Can you conclude that the median distance traveled with the additive difference from the median distance traveled with the additive? Use the $\alpha = 0.05$ level of significance.

A) a) $\mathrm { S } = 15$ b) We can not conclude that the median distances are different. B) a) $S = 12$ b) We can conclude that the median distances are different. C) a) $\mathrm { S } = 12$ b) We can not conclude that the median distances are different. D) a) $\mathrm { S } = 15$ b) We can conclude that the median distances are different. A) a) $\mathrm { S } = 15$ b) We can not conclude that the median distances are different. B) a) $S = 12$ b) We can conclude that the median distances are different. C) a) $\mathrm { S } = 12$ b) We can not conclude that the median distances are different. D) a) $\mathrm { S } = 15$ b) We can conclude that the median distances are different.

The following MINITAB output presents a multiple regression equation $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } +$ $b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 } + b _ { 4 } x _ { 4 }$ The regression equation is \[\mathrm { Y } = 1.9568 + 1.7369 \mathrm { X } 1 + 1.1099 \mathrm { X } 2 - 1.2672 \mathrm { X } 3 + 1.6080 \mathrm { X } 4\] $\begin{array}{lllll} \text { Predictor } & \text { Coef } & \text { SE Coef } & \mathrm{T} & \mathrm{P} \\ \text { Constant } & 1.9568 & 0.8248 & 1.1277 & 0.345 \\ \mathrm{X} 1 & 1.7369 & 0.7980 & 3.4296 & 0.004 \\ \mathrm{X} 2 & 1.1099 & 0.7500 & -3.2529 & 0.006 \\ \mathrm{X} 3 & -1.2672 & 0.7534 & 1.8730 & 0.076 \\ \mathrm{X} 4 & 1.6080 & 0.8733 & -0.9328 & 0.349 \end{array}$ $\mathrm{S}=2.5685 \quad \mathrm{R}-\mathrm{Sq}=33.7 \% \quad \mathrm{R}-\mathrm{Sq}(\mathrm{adj})=26.1 \%$ $\begin{array}{l} \text { Analysis of Variance }\\ \begin{array}{lcccrl} \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F P } & \\ \text { Regression } & 4 & 503.9 & 126.0 & 5.0806 & 0.003 \\ \text { Residual Error } & 40 & 990.4 & 24.8 & & \\ \text { Total } & 44 & 1494.3 & & & \\ \hline \end{array} \end{array}$ Predict the value of y when $x _ { 1 } = 1 , x _ { 2 } = 2 , x _ { 3 } = 3 , x _ { 4 } = 6$

A) 9.8031 B) 11.7599 C) 10.6228 D) 9.798 A) 9.8031 B) 11.7599 C) 10.6228 D) 9.798

Find the critical value at the $\alpha = 0.05$ level for the following sample, for testing $H _ { 0 }$ m= 41 versus $H _ { 1 } : m \neq 41$. $\begin{array} { l l l l l l l l l l l l } 57 & 61 & 55 & 50 & 35 & 52 & 58 & 22 & 41 & 48 & 32 & 27 \end{array}$

A) 4 B) 1 C) 3 D) 2 A) 4 B) 1 C) 3 D) 2

An agricultural scientist performs a 2-way ANOVA to determine the effects of three different soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following MINITAB output presents the results. $\begin{array} { l r r r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Soil Mixture } & 2 & 6.740741 & 3.37037 & 2.275 & 0.131563 \\ \text { Hybrid Variety } & 2 & 12.518519 & 6.259259 & 4.225 & 0.031306 \\ \text { Interaction } & 4 & 11.703704 & 2.925926 & 1.975 & 0.141653 \\ \text { Error } & 18 & 26.666667 & 1.481481 & & \\ \text { Total } & 26 & 57.62963 & & & \end{array}$ Can the mean effect of the soil mixture be interpreted? If so, interpret the main effect. Us $\alpha = 0.05$ level of significance.

A) Yes. Do not reject $H _ { 0 }$. B) Yes. Reject $H _ { 0 }$. C) No. A) Yes. Do not reject $H _ { 0 }$. B) Yes. Reject $H _ { 0 }$. C) No.

For the following data, compute the test statistic and the critical value, and determine whether to reject $H _ { 0 }$ at the $\alpha = 0.05$ level. $\begin{array} { l | l | l | l | l | l | l | l | l | l | l } \text { Sample A } & 76 & 61 & 71 & 80 & 77 & 78 & 63 & 60 & 77 & 79 \\ \hline \text { Sample B } & 65 & 42 & 71 & 84 & 70 & 78 & 49 & 51 & 90 & 65 \end{array}$

A) S=7 , Critical value is 4, Do not reject $H _ { 0 }$ B) S=6 , Critical value is 8, Reject $H _ { 0 }$ C) S=7 , Critical value is 4, Reject $H _ { 0 }$ D) S=6 , Critical value is 8, Do not reject $H _ { 0 }$ A) S=7 , Critical value is 4, Do not reject $H _ { 0 }$ B) S=6 , Critical value is 8, Reject $H _ { 0 }$ C) S=7 , Critical value is 4, Reject $H _ { 0 }$ D) S=6 , Critical value is 8, Do not reject $H _ { 0 }$

The following table presents the numbers of customers who - after 2 weeks of use - were satisfied $\begin{array}{ccccc} \hline & \text { Brand A } & \text { Brand B } & \text { Brand C } & \text { Brand D } \\ \hline \text { Satisfied } & 38 & 26 & 21 & 44 \\ \text { Dissatisfied } & 3 & 9 & 13 & 9 \\ \hline \end{array}$ Can you conclude that the the satisfaction rate is related to the brand of computer? Use th $\alpha = 0.05$ level of significance.

A) Reject $H _ { 0 }$. It appears that the satisfaction rates differ among the computer brands. B) Do not reject $H _ { 0 }$. There is insufficient evidence to conclude that the satisfaction rate differs among the computer brands. A) Reject $H _ { 0 }$. It appears that the satisfaction rates differ among the computer brands. B) Do not reject $H _ { 0 }$. There is insufficient evidence to conclude that the satisfaction rate differs among the computer brands.

The following MINITAB output presents a multiple regression equation $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } +$ $b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 } + b _ { 4 } x _ { 4 }$ The regression equation is \[\mathrm { Y } = 5.5079 + 1.6552 \mathrm { X } 1 - 1.1088 \mathrm { X } 2 + 1.3981 \mathrm { X } 3 - 1.2465 \mathrm { X } 4\] $\begin{array}{lllll} \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text { Constant } & 5.5079 & 0.7640 & 1.1002 & 0.314 \\ \text { X1 } & 1.6552 & 0.7032 & 3.1929 & 0.002 \\ \text { X2 } & -1.1088 & 0.6023 & -3.2310 & 0.005 \\ \text { X3 } & 1.3981 & 0.8970 & 1.8137 & 0.087 \\ \text { X4 } & -1.2465 & 0.8251 & -1.1433 & 0.354 \end{array}$ $\mathrm{S}=2.2181 \quad \mathrm{R}-\mathrm{Sq}=41.6 \% \mathrm{R}-\mathrm{Sq}(\text { adj })=35.0 \%$ $\begin{array}{l} \text { Analysis of Variance }\\ \begin{array}{lcccrr} \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F P } & \\ \text { Regression } & 4 & 637.5 & 159.4 & 7.1480 & 0.003 \\ \text { Residual Error } & 40 & 893.2 & 22.3 & & \\ \text { Total } & 44 & 1530.7 & & & \\ \hline \end{array} \end{array}$ Let $\beta _ { 1 }$ be the coefficient $X _ { 1 }$ Test the hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 1 } : \beta 1 \neq 0$ at the $\alpha = 0.05 \text { level. }$ What do you conclude?

A) Do not reject H0 B) Reject H0 A) Do not reject H0 B) Reject H0

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.45 , p _ { 2 } = 0.25$ $p _ { 3 } = 0.2 , p _ { 4 } = 0.05 , p _ { 5 } = 0.05$ $\begin{array} { l | l l l l l } \text { Category } & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Observed } & 59 & 32 & 12 & 22 & 23 \end{array}$ Compute the value of $\chi ^ { 2 }$

A) 11.070 B) 9.488 C) 76.082 D) 73.700 A) 11.070 B) 9.488 C) 76.082 D) 73.700

Exam 12: Statistical Analysis Questions in ANOVA and Rank-Sum Test

Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 7 , n _ { 2 } = 7$ and $n _ { 3 } = 5$ The sample means were $\bar { x } _ { 1 } = 1.29 , \bar { x } _ { 2 } = 1.44 , \text { and } \bar { x } _ { 3 } = 1.48$ The sample standard deviations were $s _ { 1 } = 0.30 , s _ { 2 } = 0.39 \text {, and } s _ { 3 } = 0.41$ The grand mean is $\overline { \bar { x } } = 1.395263$ Compute the value of the test statistic F .

(Multiple Choice)

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Question 101

A consumer advice web site tested a fuel additive. The distance that 12 cars could travel on five gallons of gasoline was recorded without and then with the additive. The results were as follow. Car 1 2 3 4 5 6 7 8 9 10 11 12 No Additive 176 145 124 179 139 186 180 176 90 159 92 167 With additive 186 162 130 179 149 191 193 184 105 159 94 173 a) Compute the test statistic b) Can you conclude that the median distance traveled with the additive difference from the median distance traveled with the additive? Use the $\alpha = 0.05$ level of significance.

(Multiple Choice)

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Question 102

Fill in the blank with the appropriate word or phrase. When performing the Rank-sum test we reject the null hypothesis when ?

(Multiple Choice)

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Question 103

If the test value for a signed-rank test is 7 , the sample size is 9 , and the test is to be carried out at the $\alpha = 0.10$ level of significance, should the null hypothesis be rejected? Use the table of critical values for the signed-rank test below. \alpha=0.10 \alpha=0.05 \alpha=0.02 \alpha=0.01 9 8 6 3 2 10 11 8 5 3 11 14 11 7 5 12 17 14 10 7 13 21 17 13 10

(Multiple Choice)

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Question 104

The following MINITAB output presents a multiple regression equation $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } +$ $b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 } + b _ { 4 } x _ { 4 }$ The regression equation is $\mathrm { Y } = 1.9568 + 1.7369 \mathrm { X } 1 + 1.1099 \mathrm { X } 2 - 1.2672 \mathrm { X } 3 + 1.6080 \mathrm { X } 4$ Predictor Coef SE Coef Constant 1.9568 0.8248 1.1277 0.345 1 1.7369 0.7980 3.4296 0.004 2 1.1099 0.7500 -3.2529 0.006 3 -1.2672 0.7534 1.8730 0.076 4 1.6080 0.8733 -0.9328 0.349 $\mathrm{S}=2.5685 \quad \mathrm{R}-\mathrm{Sq}=33.7 \% \quad \mathrm{R}-\mathrm{Sq}(\mathrm{adj})=26.1 \%$ Analysis of Variance Source DF SS MS F P Regression 4 503.9 126.0 5.0806 0.003 Residual Error 40 990.4 24.8 Total 44 1494.3 Predict the value of y when $x _ { 1 } = 1 , x _ { 2 } = 2 , x _ { 3 } = 3 , x _ { 4 } = 6$

(Multiple Choice)

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Question 105

Given $n _ { 1 } = 14 , n _ { 2 } = 23 , \mathrm {~S} = 307 , \text { and } H _ { 1 } : m _ { 1 } > m _ { 2 }$ compute z .

(Multiple Choice)

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Question 106

Find the critical value at the $\alpha = 0.05$ level for the following sample, for testing $H _ { 0 }$ m= 41 versus $H _ { 1 } : m \neq 41$ . 57 61 55 50 35 52 58 22 41 48 32 27

(Multiple Choice)

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Question 107

An agricultural scientist performs a 2-way ANOVA to determine the effects of three different soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following MINITAB output presents the results. Source DF SS MS F P Soil Mixture 2 6.740741 3.37037 2.275 0.131563 Hybrid Variety 2 12.518519 6.259259 4.225 0.031306 Interaction 4 11.703704 2.925926 1.975 0.141653 Error 18 26.666667 1.481481 Total 26 57.62963 Can the mean effect of the soil mixture be interpreted? If so, interpret the main effect. Us $\alpha = 0.05$ level of significance.

(Multiple Choice)

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Question 108

For the following data, compute the test statistic and the critical value, and determine whether to reject $H _ { 0 }$ at the $\alpha = 0.05$ level. Sample A 76 61 71 80 77 78 63 60 77 79 Sample B 65 42 71 84 70 78 49 51 90 65

(Multiple Choice)

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Question 109

In a one-way ANOVA, the following data were collected: SSTr=0.49, S S E=2.38 , N=22, I=5 . How many samples are there?

(Multiple Choice)

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Question 110

The following table presents the numbers of customers who - after 2 weeks of use - were satisfied Brand A Brand B Brand C Brand D Satisfied 38 26 21 44 Dissatisfied 3 9 13 9 Can you conclude that the the satisfaction rate is related to the brand of computer? Use th $\alpha = 0.05$ level of significance.

(Multiple Choice)

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Question 111

In a study of reaction times, the time to respond to a visual stimulus (x)and the

(Essay)

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Question 112

In a study of reaction times,) The regression equation is Auditory $= 174.086649 + 0.413924$ Visual Predictor Coef SE Coef T P Constant 174.086649 28.669462 6.072198 0.003717 Visual 0.413924 0.138026 2.99888 0.039987 Can you conclude that the response time to visual stimulus is useful in predicting the resp time for auditory stimulus? Answer this question using the $\alpha = 0.05$ level of significance.

(Multiple Choice)

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Question 113

The owners of a coffee stand hypothesize that the median number of sales during the hour from 10:00 AM to 11:00 AM is 2 0. They tabulated the following random sample of the number of sales during the time period. 18 24 21 17 22 23 24 22 19 22 21 23 21 16 21 Use the $\alpha = 0.05$ level of significance and provide the following to provide the fol information: a. State appropriate null and alternate hypotheses. b. Compute the test statistic. c. Find the critical value. d. State a conclusion.

(Essay)

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Question 114

Artificial hip joints consist of a ball and socket. As the joint wears, the ball (head) becomes rough. Investigators performed wear tests on metal artificial; hip joints. Joints with several different diameters were tested. The following table presents measurements of head roughness (in nanometers). Diameter Head Roughness 16 27.5 21.4 27.4 26.3 24 30.2 35.6 33.8 30 24.9 21.2 25.5 Can you conclude that the mean roughness varies with diameter? Use the $\alpha = 0.01$ level o significance.

(True/False)

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Question 115

Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 5 , n _ { 2 } = 7$ and $n _ { 3 } = 8$ The sample means were $\bar { x } _ { 1 } = 1.41 , \bar { x } _ { 2 } = 1.27 , \text { and } \bar { x } _ { 3 } = 1.76$ The sample standard deviations were $s _ { 1 } = 0.49 , s _ { 2 } = 0.47 , \text { and } s _ { 3 } = 0.25$ The grand mean is $\overline { \bar { x } } = 1.501$ Compute the sum of squares SSE.

(Multiple Choice)

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Question 116

The following MINITAB output presents a multiple regression equation $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } +$ $b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 } + b _ { 4 } x _ { 4 }$ The regression equation is $\mathrm { Y } = 5.5079 + 1.6552 \mathrm { X } 1 - 1.1088 \mathrm { X } 2 + 1.3981 \mathrm { X } 3 - 1.2465 \mathrm { X } 4$ Predictor Coef SE Coef T P Constant 5.5079 0.7640 1.1002 0.314 X1 1.6552 0.7032 3.1929 0.002 X2 -1.1088 0.6023 -3.2310 0.005 X3 1.3981 0.8970 1.8137 0.087 X4 -1.2465 0.8251 -1.1433 0.354 $\mathrm{S}=2.2181 \quad \mathrm{R}-\mathrm{Sq}=41.6 \% \mathrm{R}-\mathrm{Sq}(\text { adj })=35.0 \%$ Analysis of Variance Source DF SS MS F P Regression 4 637.5 159.4 7.1480 0.003 Residual Error 40 893.2 22.3 Total 44 1530.7 Let $\beta _ { 1 }$ be the coefficient $X _ { 1 }$ Test the hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 1 } : \beta 1 \neq 0$ at the $\alpha = 0.05 \text { level. }$ What do you conclude?

(Multiple Choice)

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Question 117

In a one-way ANOVA, the following data were collected: SSTr=0.23, S S E=2.15 , N=33, I=6 . Compute the value of the test statistic F .

(Multiple Choice)

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Question 118

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.45 , p _ { 2 } = 0.25$ $p _ { 3 } = 0.2 , p _ { 4 } = 0.05 , p _ { 5 } = 0.05$ Category 1 2 3 4 5 Observed 59 32 12 22 23 Compute the value of $\chi ^ { 2 }$

(Multiple Choice)

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Question 119

Heights, in feet, of a sample of 24 mature oak trees in a forest were measured. The results were as follows. 61 62 65 52 63 65 64 60 68 61 56 61 56 63 60 63 69 64 66 68 67 65 60 66 Can you conclude that the median height of oak trees in this forest is greater than 6 0 feet Use the $\alpha = 0.05$ level of significance. a. State appropriate null and alternate hypotheses. b. Compute the test statistic. c. Find the critical value. d. State a conclusion. feet

(Essay)

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Question 120

Fill in the blank with the appropriate word or phrase. When performing the Rank-sum test we reject the null hypothesis when ?

Given $n _ { 1 } = 14 , n _ { 2 } = 23 , \mathrm {~S} = 307 , \text { and } H _ { 1 } : m _ { 1 } > m _ { 2 }$ compute z .

Find the critical value at the $\alpha = 0.05$ level for the following sample, for testing $H _ { 0 }$ m= 41 versus $H _ { 1 } : m \neq 41$ . 57 61 55 50 35 52 58 22 41 48 32 27

For the following data, compute the test statistic and the critical value, and determine whether to reject $H _ { 0 }$ at the $\alpha = 0.05$ level. Sample A 76 61 71 80 77 78 63 60 77 79 Sample B 65 42 71 84 70 78 49 51 90 65

In a one-way ANOVA, the following data were collected: SSTr=0.49, S S E=2.38 , N=22, I=5 . How many samples are there?

In a study of reaction times, the time to respond to a visual stimulus (x)and the

In a one-way ANOVA, the following data were collected: SSTr=0.23, S S E=2.15 , N=33, I=6 . Compute the value of the test statistic F .

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.45 , p _ { 2 } = 0.25$ $p _ { 3 } = 0.2 , p _ { 4 } = 0.05 , p _ { 5 } = 0.05$ Category 1 2 3 4 5 Observed 59 32 12 22 23 Compute the value of $\chi ^ { 2 }$

Basic Ideas

Graphical Summaries of Data

Numerical Summaries of Data

Probability

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals

Hypothesis Testing

Inferences on Two Samples

Tests With Qualitative Data

Correlation and Regression

Filters

Exam 12: Statistical Analysis Questions in ANOVA and Rank-Sum Test

Fill in the blank with the appropriate word or phrase. When performing the Rank-sum test we reject the null hypothesis when ?

Given n1=14,n2=23, S=307, and H1:m1>m2n _ { 1 } = 14 , n _ { 2 } = 23 , \mathrm {~S} = 307 , \text { and } H _ { 1 } : m _ { 1 } > m _ { 2 }n1​=14,n2​=23, S=307, and H1​:m1​>m2​ compute z .

Find the critical value at the α=0.05\alpha = 0.05α=0.05 level for the following sample, for testing H0H _ { 0 }H0​ m= 41 versus H1:m≠41H _ { 1 } : m \neq 41H1​:m=41 . 57 61 55 50 35 52 58 22 41 48 32 27

For the following data, compute the test statistic and the critical value, and determine whether to reject H0H _ { 0 }H0​ at the α=0.05\alpha = 0.05α=0.05 level. Sample A 76 61 71 80 77 78 63 60 77 79 Sample B 65 42 71 84 70 78 49 51 90 65

In a one-way ANOVA, the following data were collected: SSTr=0.49, S S E=2.38 , N=22, I=5 . How many samples are there?

In a study of reaction times, the time to respond to a visual stimulus (x)and the

In a one-way ANOVA, the following data were collected: SSTr=0.23, S S E=2.15 , N=33, I=6 . Compute the value of the test statistic F .

Basic Ideas

Graphical Summaries of Data

Numerical Summaries of Data

Probability

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals

Hypothesis Testing

Inferences on Two Samples

Tests With Qualitative Data

Correlation and Regression

Filters

Given $n _ { 1 } = 14 , n _ { 2 } = 23 , \mathrm {~S} = 307 , \text { and } H _ { 1 } : m _ { 1 } > m _ { 2 }$ compute z .

Find the critical value at the $\alpha = 0.05$ level for the following sample, for testing $H _ { 0 }$ m= 41 versus $H _ { 1 } : m \neq 41$ . 57 61 55 50 35 52 58 22 41 48 32 27

For the following data, compute the test statistic and the critical value, and determine whether to reject $H _ { 0 }$ at the $\alpha = 0.05$ level. Sample A 76 61 71 80 77 78 63 60 77 79 Sample B 65 42 71 84 70 78 49 51 90 65