Use the given set of points to compute $b _ { 0 } \text { and } b _ { 1 } .$ $\begin{array} { l | l l l l l l } x & 16 & 12 & 14 & 19 & 18 & 10 \\ \hline y & 74 & 58 & 62 & 82 & 82 & 49 \end{array}$ x=12

A) $b _ { 0 } = 14.833333 ; b _ { 1 } = 10.572603$ B) $b _ { 0 } = 0 ; b _ { 1 } = 3.860274$ C) $b _ { 0 } = 10.572603 ; b _ { 1 } = 3.860274$ D) $b _ { 0 } = 3.860274 ; b _ { 1 } = 10.572603$ A) $b _ { 0 } = 14.833333 ; b _ { 1 } = 10.572603$ B) $b _ { 0 } = 0 ; b _ { 1 } = 3.860274$ C) $b _ { 0 } = 10.572603 ; b _ { 1 } = 3.860274$ D) $b _ { 0 } = 3.860274 ; b _ { 1 } = 10.572603$

Use the given set of points to construct a 95% confidence interval for $\beta _ { 1 }$ $\begin{array} { c | c c c c c c c c } x & 8 & 6 & 5 & 9 & 6 & 12 & 14 & 11 \\ \hline y & 21 & 18 & 15 & 21 & 21 & 28 & 28 & 24 \end{array}$

A) $0.8273 < \beta _ { 1 } < 1.8074$ B) $9.8187 < \beta _ { 1 } < 10.7988$ C) $0.8763 < \beta _ { 1 } < 1.7584$ D) $0.8028 < \beta _ { 1 } < 1.8319$ A) $0.8273 < \beta _ { 1 } < 1.8074$ B) $9.8187 < \beta _ { 1 } < 10.7988$ C) $0.8763 < \beta _ { 1 } < 1.7584$ D) $0.8028 < \beta _ { 1 } < 1.8319$

The number of drunk-driving arrests were counted each month by the Millville police department. $\begin{array}{cc} \hline \text { Month } & \begin{array}{c} \text { Number of } \\ \text { Drunk-Driving } \\ \text { Arrests } \end{array} \\ \hline \text { January } & 24 \\ \text { February } & 21 \\ \text { March } & 22 \\ \text { April } & 10 \\ \text { May } & 11 \\ \text { June } & 12 \\ \text { July } & 15 \\ \text { August } & 10 \\ \text { September } & 12 \\ \text { October } & 10 \\ \text { November } & 12 \\ \text { December } & 23 \\ \hline \end{array}$ Test the hypothesis that drunk-driving arrests are equally likely to occur in any month. Us $\alpha = 0.01$ level of significance.

A) Do not reject $H _ { 0 }$. The arrests may be equally likely. B) Reject $H _ { 0 }$. The arrests do not appear to be equally likely. A) Do not reject $H _ { 0 }$. The arrests may be equally likely. B) Reject $H _ { 0 }$. The arrests do not appear to be equally likely.

Use the given set of points to compute the residual standard deviation $s _ { \mathrm { e } }$ $\begin{array}{l} \begin{array} { c | l l l l l l } x & 12 & 20 & 19 & 17 & 19 & 10 \\ \hline y & 43 & 69 & 65 & 58 & 64 & 36 \end{array}\\ x = 13 \end{array}$

A) 3.191939 B) 16.166667 C) 0.730472 D) 4.230326 A) 3.191939 B) 16.166667 C) 0.730472 D) 4.230326

A biology professor claims that,) $\begin{array}{c|lllll} \text { Grade } & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Observed } & 10 & 34 & 46 & 6 & 4 \end{array}$ Test the hypothesis that the grades follow the distribution claimed by the professor. Use tl $\alpha = 0.05$ level of significance.

A) Do not reject $H _ { 0 }$. B) Reject $H _ { 0 }$. A) Do not reject $H _ { 0 }$. B) Reject $H _ { 0 }$.

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 \[\mathrm { Y } = 4.7712 + 0.2662 \mathrm { X } 1 + 1.2710 \mathrm { X } 2 - 1.1349 \mathrm { X } 3 - 1.8545 \mathrm { X } 4\] \[\mathrm { S } = 2.8844 \quad \mathrm { R } - \mathrm { Sq } = 49.6 \% \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 43.9 \%\] $\begin{array}{l} \text { Analysis of Variance }\\ \begin{array}{lcccrl} \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F P } & \\ \text { Regression } & 4 & 624.2 & 156.1 & 9.8797 & 0.003 \\ \text { Residual Error } & 40 & 633.7 & 15.8 & & \\ \text { Total } & 44 & 1257.9 & & & \end{array} \end{array}$ It is desired to drop one of the explanatory variables. Which of the following is tl appropriate action?

A) Drop $x _ { 1 }$, then see whether adjusted $R ^ { 2 }$ increases B) Drop $x _ { 1 }$, then see whether $R ^ { 2 }$ increases C) Drop $x _ { 4 }$, then see whether adjusted $R ^ { 2 }$ increases D) Drop $x _ { 4 }$, then see whether $R ^ { 2 }$ increases ost A) Drop $x _ { 1 }$, then see whether adjusted $R ^ { 2 }$ increases B) Drop $x _ { 1 }$, then see whether $R ^ { 2 }$ increases C) Drop $x _ { 4 }$, then see whether adjusted $R ^ { 2 }$ increases D) Drop $x _ { 4 }$, then see whether $R ^ { 2 }$ increases ost

For the given table of observed frequencies, perform a test for independence, using the $\alpha = 0.01$ level of significance. $\begin{array} { c c c c } \hline & 1 & 2 & 3 \\ \hline \mathrm { A } & 69 & 64 & 67 \\ \mathrm {~B} & 91 & 98 & 88 \\ \mathrm { C } & 42 & 84 & 86 \\ \hline \end{array}$

A) Do not reject $H _ { 0 }$ B) Reject $H _ { 0 }$ A) Do not reject $H _ { 0 }$ B) Reject $H _ { 0 }$

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

A sample of 10 students took a class online and 12 students took an equivalent class in a traditional classroom. Both classes were given the same final exam three weeks after the end of the courses. The scores were as follows. Online 70 87 64 95 67 81 64 74 86 80 Traditional 79 75 89 91 96 76 98 71 91 65 93 83 Can you conclude that the median score for the online class is less than for the trar class? Use the $\alpha = 0.05$ level of significance. a)State the null and alternate hypotheses. b)Compute the value of the test statistic. c)Compute the P-value. d)State a conclusion

(Essay)

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Question 41

Use the given set of points to compute $b _ { 0 } \text { and } b _ { 1 } .$ x 16 12 14 19 18 10 y 74 58 62 82 82 49 x=12

(Multiple Choice)

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Question 42

Use the given set of points to construct a 95% confidence interval for $\beta _ { 1 }$ x 8 6 5 9 6 12 14 11 y 21 18 15 21 21 28 28 24

(Multiple Choice)

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Question 43

An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together end-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond apart. For each combination of curing time and curing temperature, three tests are performed. The results of the experiment are shown below. $An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together end-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond apart. For each combination of curing time and curing temperature, three tests are performed. The results of the experiment are shown below. i). Can you reject the hypothesis of no interactions? ii). Can the main effect of curing temperature (low or high) on bonding strength bi interpreted? If so, interpret the main effect using the \alpha = 0.05 level of significance. iii). Can the main effect of curing time on bonding strength be interpreted? If so, \mathrm { i } the main effect using the \alpha = 0.05 level of significance.$ i). Can you reject the hypothesis of no interactions? ii). Can the main effect of curing temperature (low or high) on bonding strength bi interpreted? If so, interpret the main effect using the $\alpha = 0.05$ level of significance. iii). Can the main effect of curing time on bonding strength be interpreted? If so, $\mathrm { i }$ the main effect using the $\alpha = 0.05$ level of significance.

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Question 44

For a sample of size 16, the following values were obtained: $b _ { 0 } = 3.76 , b _ { 1 } = 4.21$ $s _ { \mathrm { e } } = 3.72 , \sum ( x - \bar { x } ) ^ { 2 } = 199.02 , \text { and } \bar { x } = 3.54$ Construct a 99% confidence interval for the mean response when x=1 .

(Multiple Choice)

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Question 45

Use the given set of points to test the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 1 } : \beta _ { 1 } \neq 0$ Use the $\alpha = 0.01$ level of significance. x 14 7 15 10 9 6 14 15 y 32 17 36 26 21 15 34 37

(Multiple Choice)

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Question 46

The number of drunk-driving arrests were counted each month by the Millville police department. Month Number of Drunk-Driving Arrests January 24 February 21 March 22 April 10 May 11 June 12 July 15 August 10 September 12 October 10 November 12 December 23 Test the hypothesis that drunk-driving arrests are equally likely to occur in any month. Us $\alpha = 0.01$ level of significance.

(Multiple Choice)

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Question 47

The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ . $The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis H _ { 0 } : \beta _ { 1 } = 0 . How many degrees of freedom did the calculator use?$ How many degrees of freedom did the calculator use?

(Multiple Choice)

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Question 48

Given $n _ { 1 } = 18 , n _ { 2 } = 22 , \mathrm {~S} = 311 , \text { and } H _ { 1 } : m _ { 1 } \neq m _ { 2 } \text {, }$ find the P -value.

(Multiple Choice)

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Question 49

In a one-way ANOVA, the following data were collected: SSTr=0.21, SSE=2.49 , N=24, I=3. How many degrees of freedom are there for SSE?

(Multiple Choice)

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Question 50

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether the mean fill volumes differ among the filling machines. What is the value of SSE?

(Multiple Choice)

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Question 51

Use the given set of points to compute the residual standard deviation $s _ { \mathrm { e } }$ x 12 20 19 17 19 10 y 43 69 65 58 64 36 x=13

(Multiple Choice)

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Question 52

The following table presents the numbers of customers who - after 2 weeks of use - were e Brand A Brand B Brand C Brand D Satisfied 28 22 37 47 Dissatisfied 9 16 3 12 Can you conclude that the the satisfaction rate is related to the brand of computer? the $\alpha = 0.05$ level of significance.

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Question 53

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether the mean fill volumes differ among the filling machines. What is the value of SSTr?

(Multiple Choice)

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Question 54

Given $n _ { 1 } = 15 , n _ { 2 } = 25 , \mathrm {~S} = 320.5 \text {, and } H _ { 1 } : \mu _ { 1 } \neq \mu _ { 2 }$ compute $\mu _ { s ^ { } }$

(Multiple Choice)

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Question 55

In a one-way ANOVA, the following data were collected: SSTr=0.34, S S E=2.33 , N=35, I=4 . Compute the mean squares M S E .

(Multiple Choice)

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Question 56

A biology professor claims that,) Grade 1 2 3 4 5 Observed 10 34 46 6 4 Test the hypothesis that the grades follow the distribution claimed by the professor. Use tl $\alpha = 0.05$ level of significance.

(Multiple Choice)

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Question 57

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 $\mathrm { Y } = 4.7712 + 0.2662 \mathrm { X } 1 + 1.2710 \mathrm { X } 2 - 1.1349 \mathrm { X } 3 - 1.8545 \mathrm { X } 4$ $\mathrm { S } = 2.8844 \quad \mathrm { R } - \mathrm { Sq } = 49.6 \% \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 43.9 \%$ Analysis of Variance Source DF SS MS F P Regression 4 624.2 156.1 9.8797 0.003 Residual Error 40 633.7 15.8 Total 44 1257.9 It is desired to drop one of the explanatory variables. Which of the following is tl appropriate action?

(Multiple Choice)

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Question 58

For the given table of observed frequencies, perform a test for independence, using the $\alpha = 0.01$ level of significance. 1 2 3 69 64 67 91 98 88 42 84 86

(Multiple Choice)

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Question 59

In a one-way ANOVA, the following data were collected: SSTr=0.41, S S E=2.07 , N=26, I=6 . How many degrees of freedom are there for SSTr?

(Multiple Choice)

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Question 60

Use the given set of points to compute $b _ { 0 } \text { and } b _ { 1 } .$ x 16 12 14 19 18 10 y 74 58 62 82 82 49 x=12

Use the given set of points to construct a 95% confidence interval for $\beta _ { 1 }$ x 8 6 5 9 6 12 14 11 y 21 18 15 21 21 28 28 24

For a sample of size 16, the following values were obtained: $b _ { 0 } = 3.76 , b _ { 1 } = 4.21$ $s _ { \mathrm { e } } = 3.72 , \sum ( x - \bar { x } ) ^ { 2 } = 199.02 , \text { and } \bar { x } = 3.54$ Construct a 99% confidence interval for the mean response when x=1 .

Use the given set of points to test the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 1 } : \beta _ { 1 } \neq 0$ Use the $\alpha = 0.01$ level of significance. x 14 7 15 10 9 6 14 15 y 32 17 36 26 21 15 34 37

Given $n _ { 1 } = 18 , n _ { 2 } = 22 , \mathrm {~S} = 311 , \text { and } H _ { 1 } : m _ { 1 } \neq m _ { 2 } \text {, }$ find the P -value.

In a one-way ANOVA, the following data were collected: SSTr=0.21, SSE=2.49 , N=24, I=3. How many degrees of freedom are there for SSE?

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether the mean fill volumes differ among the filling machines. What is the value of SSE?

Use the given set of points to compute the residual standard deviation $s _ { \mathrm { e } }$ x 12 20 19 17 19 10 y 43 69 65 58 64 36 x=13

The following table presents the numbers of customers who - after 2 weeks of use - were e Brand A Brand B Brand C Brand D Satisfied 28 22 37 47 Dissatisfied 9 16 3 12 Can you conclude that the the satisfaction rate is related to the brand of computer? the $\alpha = 0.05$ level of significance.

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether the mean fill volumes differ among the filling machines. What is the value of SSTr?

Given $n _ { 1 } = 15 , n _ { 2 } = 25 , \mathrm {~S} = 320.5 \text {, and } H _ { 1 } : \mu _ { 1 } \neq \mu _ { 2 }$ compute $\mu _ { s ^ { } }$

In a one-way ANOVA, the following data were collected: SSTr=0.34, S S E=2.33 , N=35, I=4 . Compute the mean squares M S E .

A biology professor claims that,) Grade 1 2 3 4 5 Observed 10 34 46 6 4 Test the hypothesis that the grades follow the distribution claimed by the professor. Use tl $\alpha = 0.05$ level of significance.

For the given table of observed frequencies, perform a test for independence, using the $\alpha = 0.01$ level of significance. 1 2 3 69 64 67 91 98 88 42 84 86

In a one-way ANOVA, the following data were collected: SSTr=0.41, S S E=2.07 , N=26, I=6 . How many degrees of freedom are there for SSTr?

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

Use the given set of points to compute b0 and b1.b _ { 0 } \text { and } b _ { 1 } .b0​ and b1​. x 16 12 14 19 18 10 y 74 58 62 82 82 49 x=12

Use the given set of points to construct a 95% confidence interval for β1\beta _ { 1 }β1​ x 8 6 5 9 6 12 14 11 y 21 18 15 21 21 28 28 24

Use the given set of points to test the null hypothesis H0:β1=0H _ { 0 } : \beta _ { 1 } = 0H0​:β1​=0 versus H1:β1≠0H _ { 1 } : \beta _ { 1 } \neq 0H1​:β1​=0 Use the α=0.01\alpha = 0.01α=0.01 level of significance. x 14 7 15 10 9 6 14 15 y 32 17 36 26 21 15 34 37

The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis H0:β1=0H _ { 0 } : \beta _ { 1 } = 0H0​:β1​=0 . How many degrees of freedom did the calculator use?

Given n1=18,n2=22, S=311, and H1:m1≠m2, n _ { 1 } = 18 , n _ { 2 } = 22 , \mathrm {~S} = 311 , \text { and } H _ { 1 } : m _ { 1 } \neq m _ { 2 } \text {, }n1​=18,n2​=22, S=311, and H1​:m1​=m2​, find the P -value.

In a one-way ANOVA, the following data were collected: SSTr=0.21, SSE=2.49 , N=24, I=3. How many degrees of freedom are there for SSE?

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether the mean fill volumes differ among the filling machines. What is the value of SSE?

Use the given set of points to compute the residual standard deviation ses _ { \mathrm { e } }se​ x 12 20 19 17 19 10 y 43 69 65 58 64 36 x=13

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether the mean fill volumes differ among the filling machines. What is the value of SSTr?

Given n1=15,n2=25, S=320.5, and H1:μ1≠μ2n _ { 1 } = 15 , n _ { 2 } = 25 , \mathrm {~S} = 320.5 \text {, and } H _ { 1 } : \mu _ { 1 } \neq \mu _ { 2 }n1​=15,n2​=25, S=320.5, and H1​:μ1​=μ2​ compute μs\mu _ { s ^ { } }μs​

In a one-way ANOVA, the following data were collected: SSTr=0.34, S S E=2.33 , N=35, I=4 . Compute the mean squares M S E .

A biology professor claims that,) Grade 1 2 3 4 5 Observed 10 34 46 6 4 Test the hypothesis that the grades follow the distribution claimed by the professor. Use tl α=0.05\alpha = 0.05α=0.05 level of significance.

For the given table of observed frequencies, perform a test for independence, using the α=0.01\alpha = 0.01α=0.01 level of significance. 1 2 3 69 64 67 91 98 88 42 84 86

In a one-way ANOVA, the following data were collected: SSTr=0.41, S S E=2.07 , N=26, I=6 . How many degrees of freedom are there for SSTr?

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

Use the given set of points to compute $b _ { 0 } \text { and } b _ { 1 } .$ x 16 12 14 19 18 10 y 74 58 62 82 82 49 x=12

Use the given set of points to construct a 95% confidence interval for $\beta _ { 1 }$ x 8 6 5 9 6 12 14 11 y 21 18 15 21 21 28 28 24

Use the given set of points to test the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 1 } : \beta _ { 1 } \neq 0$ Use the $\alpha = 0.01$ level of significance. x 14 7 15 10 9 6 14 15 y 32 17 36 26 21 15 34 37

Given $n _ { 1 } = 18 , n _ { 2 } = 22 , \mathrm {~S} = 311 , \text { and } H _ { 1 } : m _ { 1 } \neq m _ { 2 } \text {, }$ find the P -value.

Use the given set of points to compute the residual standard deviation $s _ { \mathrm { e } }$ x 12 20 19 17 19 10 y 43 69 65 58 64 36 x=13

Given $n _ { 1 } = 15 , n _ { 2 } = 25 , \mathrm {~S} = 320.5 \text {, and } H _ { 1 } : \mu _ { 1 } \neq \mu _ { 2 }$ compute $\mu _ { s ^ { } }$

A biology professor claims that,) Grade 1 2 3 4 5 Observed 10 34 46 6 4 Test the hypothesis that the grades follow the distribution claimed by the professor. Use tl $\alpha = 0.05$ level of significance.

For the given table of observed frequencies, perform a test for independence, using the $\alpha = 0.01$ level of significance. 1 2 3 69 64 67 91 98 88 42 84 86