Find the marginal frequencies for the given contingency table -The table below describes the smoking habits of a group of asthma sufferers. \[\begin{array} { l | c c c } & \text { Nonsmoker } & \text { Light smoker } & \text { Heavy smoker } \\ \hline \text { Men } & 393 & 90 & 77 \\ \text { Women } & 355 & 80 & 76 \end{array}\]

A) \[\begin{array} { r | c c c r } & \text { Non- } & \text { Light } & { \text { Heavy } } \\ & \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \\ \hline \text { Men } & 393 & 90 & 77 & 560 \\ \text { Women } & 355 & 80 & 76 & 511 \\ \text { Total } & 748 & 170 & 153 & 1071 \end{array}\] B) \[\begin{array} { r | c c c r } &\text { Non- } & \text { Light } & \text { Heavy } \\ &\text { smoker }& \text { smoker } & \text { smoker } & \text { Total } \\ \hline \text { Men } & 393 & 90 & 77 & 560 \\ \text { Women } & 355 & 80 & 76 & 511 \\ \text { Total } & 748 & 170 & 118 & 1071 \end{array}\] C) \[\begin{array} { r | c c c r } & \text { Non- } & \text { Light } & { \text { Heavy } } \\ & \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \\ \hline \text { Men } & 393 & 90 & 77 & 560 \\ \text { Women } & 355 & 80 & 76 & 583 \\ \text { Total } & 748 & 170 & 153 & 1071 \end{array}\] D) \[\begin{array} { r | c c c r } & \text { Non- } & \text { Light } & { \text { Heavy } } \\ & \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \\ \hline \text { Men } & 393 & 90 & 77 & 415 \\ \text { Women } & 355 & 80 & 76 & 511 \\ \text { Total } & 748 & 182 & 153 & 1071 \end{array}\] A) \[\begin{array} { r | c c c r } & \text { Non- } & \text { Light } & { \text { Heavy } } \\ & \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \\ \hline \text { Men } & 393 & 90 & 77 & 560 \\ \text { Women } & 355 & 80 & 76 & 511 \\ \text { Total } & 748 & 170 & 153 & 1071 \end{array}\] B) \[\begin{array} { r | c c c r } &\text { Non- } & \text { Light } & \text { Heavy } \\ &\text { smoker }& \text { smoker } & \text { smoker } & \text { Total } \\ \hline \text { Men } & 393 & 90 & 77 & 560 \\ \text { Women } & 355 & 80 & 76 & 511 \\ \text { Total } & 748 & 170 & 118 & 1071 \end{array}\] C) \[\begin{array} { r | c c c r } & \text { Non- } & \text { Light } & { \text { Heavy } } \\ & \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \\ \hline \text { Men } & 393 & 90 & 77 & 560 \\ \text { Women } & 355 & 80 & 76 & 583 \\ \text { Total } & 748 & 170 & 153 & 1071 \end{array}\] D) \[\begin{array} { r | c c c r } & \text { Non- } & \text { Light } & { \text { Heavy } } \\ & \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \\ \hline \text { Men } & 393 & 90 & 77 & 415 \\ \text { Women } & 355 & 80 & 76 & 511 \\ \text { Total } & 748 & 182 & 153 & 1071 \end{array}\]

Find the indicated expected frequency. -The contingency table below shows the results of a random sample of 400 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. \[\begin{array} { l | c c c } &{ \quad\quad\quad\quad\quad\quad\text { Opinion } } \\ \hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \\ \text { Republican } & 84 & 40 & 28 \\ \text { Democrat } & 100 & 48 & 36 \\ \text { Independent } & 20 & 32 & 12 \end{array}\] Find the expected frequency for the cell \[\mathrm { E } _ { 2,2 } \text {. }\] Round to the nearest tenth if necessary.

A) 55.2 B) 45.6 C) 93.84 D) 34.96 A) 55.2 B) 45.6 C) 93.84 D) 34.96

Find the marginal frequencies for the given contingency table -\[\begin{array}{l} \quad\quad\quad\quad\quad\text { Blood Type }\\ \begin{array} { l | c c c c } & O & \text { A } & \text { B } & \text { AB } \\ \text { Sex } & & & & \\ \hline \text { F } & 110 & 87 & 20 & 8 \\ \text { M } & 71 & 74 & 16 & 4 \end{array} \end{array}\]

A) $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Blood Type }$ $\begin{array}{|l|r|r|r|r|r|} \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\ \hline \text { F } & 110 & 87 & 20 & 8 & 225 \\ \hline \text { M } & 71 & 74 & 16 & 4 & 165 \\ \hline \text { Total } & 181 & 161 & 36 & 12 & 390\\ \hline \end{array}$ B) $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Blood Type }$ $\begin{array}{|l|r|r|r|r|r|} \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\ \hline \text { F } & 110 & 87 & 20 & 8 & 225 \\ \hline \text { M } & 71 & 74 & 16 & 4 & 160 \\ \hline \text { Total } & 181 & 161 & 36 & 12 & 390\\ \hline \end{array}$ C) $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Blood Type }$ $\begin{array}{|l|r|r|r|r|r|} \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\ \hline \text { F } & 110 & 87 & 20 & 8 & 235 \\ \hline \text { M } & 71 & 74 & 16 & 4 & 165 \\ \hline \text { Total } & 181 & 161 & 36 & 12 & 400\\ \hline \end{array}$ D) $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Blood Type }$ $\begin{array}{|l|r|r|r|r|r|} \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\ \hline \text { F } & 110 & 87 & 20 & 8 & 215 \\ \hline \text { M } & 71 & 74 & 16 & 4 & 175 \\ \hline \text { Total } & 181 & 161 & 36 & 17 & 390\\ \hline \end{array}$ A) $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Blood Type }$ $\begin{array}{|l|r|r|r|r|r|} \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\ \hline \text { F } & 110 & 87 & 20 & 8 & 225 \\ \hline \text { M } & 71 & 74 & 16 & 4 & 165 \\ \hline \text { Total } & 181 & 161 & 36 & 12 & 390\\ \hline \end{array}$ B) $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Blood Type }$ $\begin{array}{|l|r|r|r|r|r|} \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\ \hline \text { F } & 110 & 87 & 20 & 8 & 225 \\ \hline \text { M } & 71 & 74 & 16 & 4 & 160 \\ \hline \text { Total } & 181 & 161 & 36 & 12 & 390\\ \hline \end{array}$ C) $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Blood Type }$ $\begin{array}{|l|r|r|r|r|r|} \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\ \hline \text { F } & 110 & 87 & 20 & 8 & 235 \\ \hline \text { M } & 71 & 74 & 16 & 4 & 165 \\ \hline \text { Total } & 181 & 161 & 36 & 12 & 400\\ \hline \end{array}$ D) $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Blood Type }$ $\begin{array}{|l|r|r|r|r|r|} \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\ \hline \text { F } & 110 & 87 & 20 & 8 & 215 \\ \hline \text { M } & 71 & 74 & 16 & 4 & 175 \\ \hline \text { Total } & 181 & 161 & 36 & 17 & 390\\ \hline \end{array}$

Exam 10: Chi-Square Tests and the F-Distribution

Find the critical value $\mathrm { F } _ { 0 }$ to test the claim that $\sigma \underset { 1 } { 2 } \neq \sigma _{ 2 }^{ 2 }$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $\alpha = 0.02$ =11 =18 =0.578 =0.260

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Question 1

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Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are independent and that each population has a normal distribution. -Test the claim that $\sigma _ { 1 } ^ { 2 } \leq \sigma { } _ { 2 } ^ { 2 } \text {. }$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $\alpha = 0.05 \text {. }$ =16 =15 =21.866 =20.384

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Question 2

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$\mathrm { H } _ { 0 } : \sigma _ { 1 } ^ { 2 } \leq \sigma _ { 2 } ^ { 2 } \text { (claim) }$ $\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } > \sigma_ 2^2$ Critical value $\mathrm { F } _ { 0 }$ = 2.46; rejection region F $>$ 2.46
Test statistic F $\approx$ 1.073;
Fail to reject H₀; There is not sufficient evidence at the 5% significance level to reject the claim that . $\sigma _ { 1 } ^ { 2 } \leq \sigma _ { 2 } ^ { 2 }$

A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for The 45-65 group, and 12% for the group over 65. Calculate the chi-square test statistic χ $\chi ^ { 2 }$ to test the claim that All ages have crash rates proportional to their driving rates. Age Under 26 26-45 46-65 Over 65 Drivers 66 39 25 30

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Question 3

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A

Find the left-tailed and right-tailed critical F-values for a two-tailed test. Use the sample statistics below. Let $\alpha$ α = 0.05. =5 =6 =5.8 =2.7

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Question 4

A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and The results are given below. Find the critical value χ $\chi _ { 0 } ^ { 2 }$ to test the claim that walking and low, moderate, and High blood pressure are not related. Use $\alpha$ = 0.01. Blood Pressure Low Moderate High Walkers 35 62 25 Non-walkers 21 65 28

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Question 5

Find the indicated expected frequency. -A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and The results are given below. Find the expected frequency $\mathrm { E } _ { 2,2 }$ to test the claim that walking and low, moderate, And high blood pressure are not related. Round to the nearest tenth if necessary. Blood Pressure Low Moderate High Walkers 38 64 20 Non-walkers 24 63 27

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Question 6

Perform the indicated one-way ANOVA test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic F. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that each population is normally distributed and that the population variances are equal. -A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six weeks, each subjectʹs blood pressure is recorded. Test the claim that there is no difference among the means. Use $\alpha = 0.05 .$ Group 1 Group 2 Group 3 11 8 6 12 2 12 13 3 4 15 5 8 9 4 9 8 0 4

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Question 7

Calculate the test statistic F to test the claim that $\sigma _ { 1 } ^ { 2 } > \sigma { } _ { 2 } ^ { 2 } .$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. =16 =13 =4800 =1875

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Question 8

A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 46-65 group, and 12% for the group over 65. Test the claim that all ages have crash rates proportional to their driving rates. Use $\alpha$ = 0.05. Age Under 26 26-45 46-65 Over 65 Drivers 66 39 25 30

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Question 9

Find the marginal frequencies for the given contingency table -The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker Light smoker Heavy smoker Men 393 90 77 Women 355 80 76

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Question 10

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are independent and that each population has a normal distribution. -A medical researcher suspects that the variance of the pulse rate of smokers is higher than the variance of the pulse rate of non-smokers. Use the sample statistics below to test the researcherʹs suspicion. Use $\alpha$ α = 0.05. Smokers =61 1=7.8 Non-smokers =121 =5.3

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Question 11

Perform the indicated one-way ANOVA test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic F. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that each population is normally distributed and that the population variances are equal. -A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected from each group. Their ages are recorded below. Test the claim that at least one mean is different from the others. Use $\alpha = 0.01 \text {. }$ Elementary Teachers High School Teachers Community College Teachers 23 41 39 28 36 45 27 38 36 25 47 61 52 42 45 37 31 35

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Question 12

Find the indicated expected frequency. -A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given Below. Find the expected frequency for $\mathrm { E } _ { 2,2 }$ tto test the claim that the number of home team and visiting team Wins are independent of the sport. Round to the nearest tenth if necessary. Football Basketball Soccer Baseball Home team wins 41 154 27 81 Visiting team wins 30 98 20 75

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Question 13

Find the indicated expected frequency. -The contingency table below shows the results of a random sample of 400 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Opinion Party Approve Disapprove No Opinion Republican 84 40 28 Democrat 100 48 36 Independent 20 32 12 Find the expected frequency for the cell $\mathrm { E } _ { 2,2 } \text {. }$ Round to the nearest tenth if necessary.

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Question 14

A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Calculate the chi -square Test statistic χ $\chi ^ { 2 }$ to determine if there is enough evidence to conclude that the number of minutes spent online Per day is related to gender. Minutes spent online per day Gender 0-30 30-60 60-90 90+ Male 25 35 75 45 Female 30 45 45 15

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Question 15

A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and The results are given below. Calculate the chi-square test statistic χ $\chi ^ { 2 }$ to test the claim that walking and low, Moderate, and high blood pressure are not related. Blood Pressure Low Moderate High Walkers 35 62 25 Non-walkers 21 65 28

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Question 16

Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on Until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting Positions. Calculate the chi-square test statistic χ $\chi ^ { 2 }$ to test the claim that the number of wins is uniformly Distributed across the different starting positions. The results are based on 240 wins. Starting Position 1 2 3 4 5 6 Number of Wins 45 36 33 50 32 44

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Question 17

A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given Below. Find the critical value χ $\chi _ { 0 } ^ { 2 }$ to test the claim that the number of home team and visiting team wins is Independent of the sport. Use $\alpha$ = 0.01. Football Basketball Soccer Baseball Home team wins 39 156 25 83 Visiting team wins 31 98 19 75

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Question 18

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are independent and that each population has a normal distribution. -A random sample of 21 women had blood pressure levels with a variance of 553.6. A random sample of 18 men had blood pressure levels with a variance of 368.64. Test the claim that the blood pressure levels for women have a larger variance than those for men. Use $\alpha = 0.01 .$

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Question 19

Find the marginal frequencies for the given contingency table - Blood Type O A B AB Sex F 110 87 20 8 M 71 74 16 4

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Question 20

Find the critical value $\mathrm { F } _ { 0 }$ to test the claim that $\sigma \underset { 1 } { 2 } \neq \sigma _{ 2 }^{ 2 }$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $\alpha = 0.02$ =11 =18 =0.578 =0.260

Find the left-tailed and right-tailed critical F-values for a two-tailed test. Use the sample statistics below. Let $\alpha$ α = 0.05. =5 =6 =5.8 =2.7

Calculate the test statistic F to test the claim that $\sigma _ { 1 } ^ { 2 } > \sigma { } _ { 2 } ^ { 2 } .$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. =16 =13 =4800 =1875

Find the marginal frequencies for the given contingency table -The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker Light smoker Heavy smoker Men 393 90 77 Women 355 80 76

Find the marginal frequencies for the given contingency table - Blood Type O A B AB Sex F 110 87 20 8 M 71 74 16 4

Introduction to Statistics

Descriptive Statistics

Probability

Discrete Probability Distributions

Normal Probability Distributions

Confidence Intervals

Hypothesis Testing With One Sample

Hypothesis Testing With Two Samples

Correlation and Regression

Nonparametric Tests Online and CD Only

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Exam 10: Chi-Square Tests and the F-Distribution

Find the left-tailed and right-tailed critical F-values for a two-tailed test. Use the sample statistics below. Let α\alphaα α = 0.05. =5 =6 =5.8 =2.7

Calculate the test statistic F to test the claim that σ12>σ22.\sigma _ { 1 } ^ { 2 } > \sigma { } _ { 2 } ^ { 2 } .σ12​>σ22​. Two samples are randomly selected from populations that are normal. The sample statistics are given below. =16 =13 =4800 =1875

Find the marginal frequencies for the given contingency table -The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker Light smoker Heavy smoker Men 393 90 77 Women 355 80 76

Find the marginal frequencies for the given contingency table - Blood Type O A B AB Sex F 110 87 20 8 M 71 74 16 4

Introduction to Statistics

Descriptive Statistics

Probability

Discrete Probability Distributions

Normal Probability Distributions

Confidence Intervals

Hypothesis Testing With One Sample

Hypothesis Testing With Two Samples

Correlation and Regression

Nonparametric Tests Online and CD Only

Filters

Find the left-tailed and right-tailed critical F-values for a two-tailed test. Use the sample statistics below. Let $\alpha$ α = 0.05. =5 =6 =5.8 =2.7

Calculate the test statistic F to test the claim that $\sigma _ { 1 } ^ { 2 } > \sigma { } _ { 2 } ^ { 2 } .$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. =16 =13 =4800 =1875