\[\text { In comparing the two variances below, what is the test value and what are the degrees of freedom that }\] $\begin{array}{|l|c|c|} \hline & \text { Variance } & \text { Number of values } \\ \hline \text { Sample 1 } & 5 & 19 \\ \hline \text { Sample 2 } & 11 & 29 \\ \hline \end{array}$

A) test value = 0.45, degrees of freedom = 19 and 29 B) test value = 0.45, degrees of freedom = 18 and 28 C) test value = 2.20, degrees of freedom = 28 and 18 D) test value = 2.20, degrees of freedom = 29 and 19 A) test value = 0.45, degrees of freedom = 19 and 29 B) test value = 0.45, degrees of freedom = 18 and 28 C) test value = 2.20, degrees of freedom = 28 and 18 D) test value = 2.20, degrees of freedom = 29 and 19

A marketing firm asked a random set of married and single men how much they were willing to spend for a vacation. At ${ } ^ { \star } = .05$, is a difference in the two amounts? $\begin{array}{|l|c|c|} \hline & \text { Married men } & \text { Single men } \\ \hline \text { Sample size } & 80 & 60 \\ \hline \text { Mean spending } & 380 & 325 \\ \hline \text { Sample variance } & 6000 & 8000 \\ \hline \end{array}$

A) No, because the test value 0.26 is inside the interval (-1.96, 1.96) B) Yes, because the test value 3.81 is outside the interval (-1.96, 1.96) C) Yes, because the test value 1.33 is inside the interval (-1.96, 1.96) D) No, because the test value 1.33 is outside the interval (-1.96, 1.96) A) No, because the test value 0.26 is inside the interval (-1.96, 1.96) B) Yes, because the test value 3.81 is outside the interval (-1.96, 1.96) C) Yes, because the test value 1.33 is inside the interval (-1.96, 1.96) D) No, because the test value 1.33 is outside the interval (-1.96, 1.96)

In comparing the two standard deviations below, what is the test value and what are the degrees of freedom that should be used? \[\begin{array} { | l | c | c | } \hline & \text { Standard Deviation } & \text { Number of values } \\ \hline \text { Sample 1 } & 7 & 17 \\ \hline \text { Sample 2 } & 2 & 25 \\ \hline \end{array}\]

A) test value = 3.50, degrees of freedom = 17 and 25 B) test value = 3.50, degrees of freedom = 16 and 24 C) test value = 12.25, degrees of freedom = 17 and 25 D) test value = 12.25, degrees of freedom = 16 and 24 A) test value = 3.50, degrees of freedom = 17 and 25 B) test value = 3.50, degrees of freedom = 16 and 24 C) test value = 12.25, degrees of freedom = 17 and 25 D) test value = 12.25, degrees of freedom = 16 and 24

\[\begin{array}{l} \text { In testing the equality of the two means below, what is the test statistic? (Use the unequal variances }\\ \begin{array} { | l | c | c | } \hline & \text { Sample 1 } & \text { Sample 2 } \\ \hline \text { Sample size } & 8 & 13 \\ \hline \text { Sample mean } & 80 & 115 \\ \hline \text { Sample variance } & 450 & 100 \\ \hline \end{array} \end{array}\]

A) -2.36 B) -0.22 C) -0.55 D) -4.38 A) -2.36 B) -0.22 C) -0.55 D) -4.38

\[\begin{array}{l} \text { In testing the equality of the two means below, what is the test statistic? (Use the equal variances }\\ \begin{array} { | l | c | c | } \hline & \text { Sample 1 } & \text { Sample 2 } \\ \hline \text { Sample size } & 12 & 9 \\ \hline \text { Sample mean } & 115 & 80 \\ \hline \text { Sample variance } & 700 & 400 \\ \hline \end{array} \end{array}\]

A) 3.31 B) 1.75 C) 0.31 D) 2.31 A) 3.31 B) 1.75 C) 0.31 D) 2.31

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. \[\begin{array} { | l | l | } \hline \text { Miles / Gal Without } & \text { Miles / Gal With } \\ \hline 21.2 & 23.8 \\ \hline 25.4 & 25.6 \\ \hline 20.9 & 22.4 \\ \hline 27.6 & 28.3 \\ \hline 22.8 & 24.5 \\ \hline 27.3 & 28.8 \\ \hline 23.4 & 25.2 \\ \hline \end{array}\] -State the alternative hypothesis.

A) $H _ { 1 } : \mu _ { D } = 0$ B) $H _ { 1 } : \mu _ { D } > 0$ C) $H _ { 1 } , \mu _ { D } 0$ C) $H _ { 1 } , \mu _ { D } < 0$ D) $H _ { 1 } = \mu _ { D } = 0$

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. \[\begin{array} { | l | l | } \hline \text { Miles / Gal Without } & \text { Miles / Gal With } \\ \hline 21.2 & 23.8 \\ \hline 25.4 & 25.6 \\ \hline 20.9 & 22.4 \\ \hline 27.6 & 28.3 \\ \hline 22.8 & 24.5 \\ \hline 27.3 & 28.8 \\ \hline 23.4 & 25.2 \\ \hline \end{array}\] -Determine the mean of the difference.

A) -0.96 B) -6.3 C) 1.43 D) -1.43 A) -0.96 B) -6.3 C) 1.43 D) -1.43

A bond analyst is analyzing the interest rates for equivalent provincial bonds and Canada bonds. At $\ddagger = .05$, is there a difference in the interest rates paid? $\begin{array}{|l|c|c|} \hline & \text { Canada bonds } & \text { Provincial bonds } \\ \hline \text { Sample size } & 80 & 40 \\ \hline \text { Mean interest rate }(\%) & 3.9 & 4.15 \\ \hline \text { Sample variance } & 0.01 & 0.03 \\ \hline \end{array}$

A) Yes, because the test value -8.45 is outside the interval (-1.96, 1.96) B) Yes, because the test value -2.86 is outside the interval (-1.96, 1.96) C) Yes, because the test value 71.43 is outside the interval (-1.96, 1.96) D) No, because the test value -0.03 is inside the interval (-1.96, 1.96) A) Yes, because the test value -8.45 is outside the interval (-1.96, 1.96) B) Yes, because the test value -2.86 is outside the interval (-1.96, 1.96) C) Yes, because the test value 71.43 is outside the interval (-1.96, 1.96) D) No, because the test value -0.03 is inside the interval (-1.96, 1.96)

Exam 8: Testing the Difference Between Two Means, Two Proportions, and Two Variances

$\text { In comparing the two variances below, what is the test value and what are the degrees of freedom that }$ Variance Number of values Sample 1 5 19 Sample 2 11 29

(Multiple Choice)

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Question 21

The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of freedom = 7 and $a = 0.025$

(Short Answer)

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Question 22

An educational researcher is analyzing the test scores for statistics students taught using two different methods - a traditional method and a web-based, self-paced method. Can he conclude, at $\ddagger = .05$ , that the test scores in the web-based, self-paced method are lower? Traditional Web-based Self-paced Sample size 80 60 Mean test score 86 84 Sample variance 24 46

(Multiple Choice)

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Question 23

A conservationist wants to know if the water level (in meters) in Crab Lake is more or less variable than the water level in Gull Lake. If one tested the hypothesis that the levels are equally variable at $\alpha = 0.05$ , the hypothesis would be Crag Lake Gull Lake 44 33 8 3.9 2.4 \| 22 21 ________________________________________

(Short Answer)

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Question 24

A marketing firm asked a random set of married and single men how much they were willing to spend for a vacation. At ${ } ^ { \star } = .05$ , is a difference in the two amounts? Married men Single men Sample size 80 60 Mean spending 380 325 Sample variance 6000 8000

(Multiple Choice)

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Question 25

Samples are independent when they are not related.

(True/False)

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Question 26

A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at ${ } ^ { \pm } = .10$ , that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree? Pine trees Spruce trees Sample size 80 60 Mean trunk diameter () 35 33 Sample variance 130 150

(Multiple Choice)

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Question 27

A study on the oxygen consumption rate (OCR) of sea cucumbers involved a random sample of size 10 at 15oC and a second random sample of size 7 kept at 18oC. If one tested the hypothesis that this range Of temperature had no effect on the OCR, the degrees of freedom for the test statistic would be (assume Equal variability)

(Multiple Choice)

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Question 28

In comparing the two standard deviations below, what is the test value and what are the degrees of freedom that should be used? Standard Deviation Number of values Sample 1 7 17 Sample 2 2 25

(Multiple Choice)

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Question 29

In testing the equality of the two means below, what is the test statistic? (Use the unequal variances Sample 1 Sample 2 Sample size 8 13 Sample mean 80 115 Sample variance 450 100

(Multiple Choice)

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Question 30

Calculate the critical value. Use $a = 0.05$ Refer To: 09-18

(Multiple Choice)

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Question 31

In testing the equality of the two means below, what is the test statistic? (Use the equal variances Sample 1 Sample 2 Sample size 12 9 Sample mean 115 80 Sample variance 700 400

(Multiple Choice)

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Question 32

One of the requirements for the z - test for comparing two proportions is that the samples must be dependent on each other.

(True/False)

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Question 33

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Miles / Gal Without Miles / Gal With 21.2 23.8 25.4 25.6 20.9 22.4 27.6 28.3 22.8 24.5 27.3 28.8 23.4 25.2 -State the alternative hypothesis.

(Multiple Choice)

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Question 34

A local charity thinks that people in River Heights give more money to their charity than people in Lakeview. They conducted a survey of 24 people in each subdivision and recorded the results. Is their $\text { hypothesis correct? Let } \alpha=0.01 \text {. }$ $A local charity thinks that people in River Heights give more money to their charity than people in Lakeview. They conducted a survey of 24 people in each subdivision and recorded the results. Is their \text { hypothesis correct? Let } \alpha=0.01 \text {. }$

(Essay)

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Question 35

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Miles / Gal Without Miles / Gal With 21.2 23.8 25.4 25.6 20.9 22.4 27.6 28.3 22.8 24.5 27.3 28.8 23.4 25.2 -Determine the mean of the difference.

(Multiple Choice)

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Question 36

A bond analyst is analyzing the interest rates for equivalent provincial bonds and Canada bonds. At $\ddagger = .05$ , is there a difference in the interest rates paid? Canada bonds Provincial bonds Sample size 80 40 Mean interest rate (\%) 3.9 4.15 Sample variance 0.01 0.03

(Multiple Choice)

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Question 37

When comparing two variances or standard deviations, a f -test is used.

(True/False)

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Question 38

A medical researcher is interested in whether patients' left arms or right arms are longer. If 9 patients participate in this study (so that 9 left arms and 9 right arms are measured), how many degrees of freedom Should the researcher use in her t-test critical value?

(Multiple Choice)

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Question 39

A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount of money spent on lunches. The variance of nine business dinners was $6.12, and the Variance of 12 business lunches was $0.87. What is the test value?

(Multiple Choice)

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Question 40

$\text { In comparing the two variances below, what is the test value and what are the degrees of freedom that }$ Variance Number of values Sample 1 5 19 Sample 2 11 29

The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of freedom = 7 and $a = 0.025$

A marketing firm asked a random set of married and single men how much they were willing to spend for a vacation. At ${ } ^ { \star } = .05$ , is a difference in the two amounts? Married men Single men Sample size 80 60 Mean spending 380 325 Sample variance 6000 8000

Samples are independent when they are not related.

In comparing the two standard deviations below, what is the test value and what are the degrees of freedom that should be used? Standard Deviation Number of values Sample 1 7 17 Sample 2 2 25

In testing the equality of the two means below, what is the test statistic? (Use the unequal variances Sample 1 Sample 2 Sample size 8 13 Sample mean 80 115 Sample variance 450 100

Calculate the critical value. Use $a = 0.05$ Refer To: 09-18

In testing the equality of the two means below, what is the test statistic? (Use the equal variances Sample 1 Sample 2 Sample size 12 9 Sample mean 115 80 Sample variance 700 400

One of the requirements for the z - test for comparing two proportions is that the samples must be dependent on each other.

A bond analyst is analyzing the interest rates for equivalent provincial bonds and Canada bonds. At $\ddagger = .05$ , is there a difference in the interest rates paid? Canada bonds Provincial bonds Sample size 80 40 Mean interest rate (\%) 3.9 4.15 Sample variance 0.01 0.03

When comparing two variances or standard deviations, a f -test is used.

A medical researcher is interested in whether patients' left arms or right arms are longer. If 9 patients participate in this study (so that 9 left arms and 9 right arms are measured), how many degrees of freedom Should the researcher use in her t-test critical value?

A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount of money spent on lunches. The variance of nine business dinners was $6.12, and the Variance of 12 business lunches was $0.87. What is the test value?

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Correlation and Regression

Chi-Square and Analysis of Variance Anova

Tables

Data Bank

Glossary

Filters

Exam 8: Testing the Difference Between Two Means, Two Proportions, and Two Variances

The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of freedom = 7 and a=0.025a = 0.025a=0.025

A marketing firm asked a random set of married and single men how much they were willing to spend for a vacation. At ⋆=.05{ } ^ { \star } = .05⋆=.05 , is a difference in the two amounts? Married men Single men Sample size 80 60 Mean spending 380 325 Sample variance 6000 8000

Samples are independent when they are not related.

In comparing the two standard deviations below, what is the test value and what are the degrees of freedom that should be used? Standard Deviation Number of values Sample 1 7 17 Sample 2 2 25

In testing the equality of the two means below, what is the test statistic? (Use the unequal variances Sample 1 Sample 2 Sample size 8 13 Sample mean 80 115 Sample variance 450 100

Calculate the critical value. Use a=0.05a = 0.05a=0.05 Refer To: 09-18

In testing the equality of the two means below, what is the test statistic? (Use the equal variances Sample 1 Sample 2 Sample size 12 9 Sample mean 115 80 Sample variance 700 400

One of the requirements for the z - test for comparing two proportions is that the samples must be dependent on each other.

A bond analyst is analyzing the interest rates for equivalent provincial bonds and Canada bonds. At ‡=.05\ddagger = .05‡=.05 , is there a difference in the interest rates paid? Canada bonds Provincial bonds Sample size 80 40 Mean interest rate (\%) 3.9 4.15 Sample variance 0.01 0.03

When comparing two variances or standard deviations, a f -test is used.

A medical researcher is interested in whether patients' left arms or right arms are longer. If 9 patients participate in this study (so that 9 left arms and 9 right arms are measured), how many degrees of freedom Should the researcher use in her t-test critical value?

A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount of money spent on lunches. The variance of nine business dinners was $6.12, and the Variance of 12 business lunches was $0.87. What is the test value?

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Correlation and Regression

Chi-Square and Analysis of Variance Anova

Tables

Data Bank

Glossary

Filters

The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of freedom = 7 and $a = 0.025$

A marketing firm asked a random set of married and single men how much they were willing to spend for a vacation. At ${ } ^ { \star } = .05$ , is a difference in the two amounts? Married men Single men Sample size 80 60 Mean spending 380 325 Sample variance 6000 8000

Calculate the critical value. Use $a = 0.05$ Refer To: 09-18

A bond analyst is analyzing the interest rates for equivalent provincial bonds and Canada bonds. At $\ddagger = .05$ , is there a difference in the interest rates paid? Canada bonds Provincial bonds Sample size 80 40 Mean interest rate (\%) 3.9 4.15 Sample variance 0.01 0.03