Use the following set of observed frequencies to test the independence of the two variables.Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. \[\begin{array} { | l | l | l | l | } \hline & \mathrm { C } & \mathrm { D } & \mathrm { E } \\ \hline \mathrm { A } & 12 & 10 & 8 \\ \hline \mathrm { B } & 20 & 24 & 26 \\ \hline \end{array}\] Using $\alpha$= 0.05, the critical chi-square value is _______.

A) 9.488 B) 1.386 C) 8.991 D) 3.357 E) 5.991 A) 9.488 B) 1.386 C) 8.991 D) 3.357 E) 5.991 E

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles.The following is a contingency table from a random sample of 385 individuals: $\begin{array}{c} \begin{array}{|l|} \hline \\ \hline 18-25 \\ \hline 26-35 \\ \hline 36-45 \\ \hline 46+ \\ \hline \end{array} \begin{array}{l} \hline\text { Style } -{1}\\ \hline 125 \\ \hline 87 \\ \hline 50 \\ \hline 12 \\ \hline \end{array} \begin{array}{|l|} \hline \text { Style}-2 \\ \hline 13 \\ \hline 12 \\ \hline 22 \\ \hline 25 \\ \hline \end{array} \begin{array}{l|} \hline\text { Style}-3 \\ \hline 6 \\ \hline 6 \\ \hline 12 \\ \hline 15\\ \hline \end{array} \end{array}$ The researcher uses $\alpha$= 0.05.The appropriate decision is ______.

A) reject the null hypothesis and conclude the two variables are not independent B) reject the null hypothesis and conclude the two variables are independent C) do not reject the null hypothesis and conclude the two variables are not independent D) do not reject the null hypothesis and conclude the two variables are independent E) do nothing A) reject the null hypothesis and conclude the two variables are not independent B) reject the null hypothesis and conclude the two variables are independent C) do not reject the null hypothesis and conclude the two variables are not independent D) do not reject the null hypothesis and conclude the two variables are independent E) do nothing A

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles.The following is a contingency table from a random sample of 385 individuals: $\begin{array}{c} \begin{array}{|l|} \hline \\ \hline 18-25 \\ \hline 26-35 \\ \hline 36-45 \\ \hline 46+ \\ \hline \end{array} \begin{array}{l} \hline\text { Style } -{1}\\ \hline 125 \\ \hline 87 \\ \hline 50 \\ \hline 12 \\ \hline \end{array} \begin{array}{|l|} \hline \text { Style}-2 \\ \hline 13 \\ \hline 12 \\ \hline 22 \\ \hline 25 \\ \hline \end{array} \begin{array}{l|} \hline\text { Style}-3 \\ \hline 6 \\ \hline 6 \\ \hline 12 \\ \hline 15\\ \hline \end{array} \end{array}$ The researcher uses$\alpha$ = 0.05.The observed chi-square value is ______.

A) 86.59 B) 88.64 C) 89.59 D) 89.64 E) 90.59 A) 86.59 B) 88.64 C) 89.59 D) 89.64 E) 90.59

Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis. \[\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Cars per 15-rrirute iriterval } & 0 & 1 & 2 & 3 & 4 & \geq 5 \\ \hline \text { Observed frequency } & 5 & 15&17 & 12& 10 & 8 \\ \hline \end{array}\] Using$\alpha$ = 0.05, the critical value of chi-square for this goodness-of-fit test is ____.

A) 9.49 B) 7.81 C) 7.78 D) 11.07 E) 12.77 A) 9.49 B) 7.81 C) 7.78 D) 11.07 E) 12.77

A researcher believes that a variable is Poisson distributed across six categories.To test this, the following random sample of observations is collected: \[\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Categary } & 0 & 1 & 2 & 3 & 4 & \geq 5 \\ \hline \text { Observed } & 7 & 18 & 25 & 17 & 12 & 5 \\ \hline \end{array}\] Using $\alpha$ = 0.10, the critical value of chi-square for the data is _______.

A) 9.236 B) 7.779 C) 13.277 D) 12.89 E) 1.064 A) 9.236 B) 7.779 C) 13.277 D) 12.89 E) 1.064

Exam 16: Analysis of Categorical Data

A researcher is interested in using a chi-square test of independence to determine if age is independent of minutes spent reading.Age is divided into four categories while minutes spent reading is classified as high, medium, low.The number of degrees of freedom for this test is 12.

Free

(True/False)

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Question 1

Correct Answer:

Verified

False

Use the following set of observed frequencies to test the independence of the two variables.Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. 12 10 8 20 24 26 Using $\alpha$ = 0.05, the critical chi-square value is _______.

Free

(Multiple Choice)

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(34)

Question 2

Correct Answer:

Verified

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles.The following is a contingency table from a random sample of 385 individuals: 18-25 26-35 36-45 46+ Style - 1 125 87 50 12 Style -2 13 12 22 25 Style -3 6 6 12 15 The researcher uses $\alpha$ = 0.05.The appropriate decision is ______.

Free

(Multiple Choice)

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(38)

Question 3

Correct Answer:

Verified

A recent national poll showed the reading habits of adults during the last 12 months: 3 or more books 5 2 boxlss 27 1 book 38 No hooks 30 A poll in a small Midwestern town shows the following percentages: 3 or more broks 1 2 books 22 1 boxk 39 No hooks 38 Using $\alpha$ = .05, the critical value of the chi-squared goodness-of-fit statistic is ______.

(Multiple Choice)

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Question 4

When using the chi-square goodness-of-fit test, the type of distribution (uniform, Poisson, normal)being used does not influence the hypothesis test.

(True/False)

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Question 5

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages.She wonders whether acceptance is influenced by the age of the children in the household.Her staff prepared the following contingency table from a random sample of 100 households. Catherine's null hypothesis is ______________.

(Multiple Choice)

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Question 6

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals. The estimate of the expected number of individuals with income less than $30,000 who purchase regular gasoline when income and type of gasoline are independent is _______.

(Multiple Choice)

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Question 7

A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a uniform distribution for a dataset with "k" categories.This test has (k-3)degrees of freedom.

(True/False)

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Question 8

Anita Cruz recently assumed responsibility for a large investment portfolio.She wonders whether the industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks. Anita's null hypothesis is ______________.

(Multiple Choice)

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Question 9

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals. $A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals. Using \alpha = .01, critical chi-square value is .$ Using $\alpha$ = .01, critical chi-square value is .

(Multiple Choice)

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Question 10

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles.The following is a contingency table from a random sample of 385 individuals: 18-25 26-35 36-45 46+ Style - 1 125 87 50 12 Style -2 13 12 22 25 Style -3 6 6 12 15 The researcher uses $\alpha$ = 0.05.The observed chi-square value is ______.

(Multiple Choice)

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Question 11

A suburban realtor is studying commuter time in the Houston metropolitan area.She has been told the average weekday travel time from a southern suburb at 8:00am is 45 minutes.For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00am.She expects that data are uniformly distributed across the five months.Her sample of observed data yields the following frequencies 9 days, 15 days, 8 days, 11 days, 12 days.Using $\alpha$ = .01, the observed chi-square value is _______.

(Multiple Choice)

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Question 12

A market researcher is studying the use of coupons by consumers of varying ages.She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out.It is expected that data are uniformly distributed across the four age categories.The observed data results in frequencies of 22, 35, 32, and 21.Using $\alpha$ = .05, the critical chi-square value is _______.

(Multiple Choice)

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Question 13

Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis. Cars per 15-rrirute iriterval 0 1 2 3 4 \geq5 Observed frequency 5 15 17 12 10 8 Using $\alpha$ = 0.05, the critical value of chi-square for this goodness-of-fit test is ____.

(Multiple Choice)

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Question 14

A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution.There are 8 categories, and lambda must be estimated.Alpha is chosen to be 0.10.The critical (table)value of chi-square is _______.

(Multiple Choice)

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Question 15

A goodness of fit test is to be performed to see if consumers prefer any of three package designs (A, B, and C)more than the other two.A sample of 60 consumers is used.What is the expected frequency for category A?

(Multiple Choice)

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Question 16

In a college dining hall, students with a full meal plan can eat up to four meals each day.The kitchen would like to know the distribution of meal consumption by students and think it would follow a Poisson distribution.Reviewing dining hall data over the past week, the following information is compiled. Meals 0 1 2 3 \geq4 Observed frequency 287 581 447 290 185 Using $\alpha$ =0.05, the appropriate decision for this goodness of fit test is _______.

(Multiple Choice)

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Question 17

A test of independence is to be performed.The contingency table has 4 rows and 5 columns.What would the degrees of freedom be?

(Multiple Choice)

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Question 18

A variable contains five categories.It is expected that data are uniformly distributed across these five categories.To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24.Using $\alpha$ = .01, the observed value of chi-square is _______.

(Multiple Choice)

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Question 19

A researcher believes that a variable is Poisson distributed across six categories.To test this, the following random sample of observations is collected: Categary 0 1 2 3 4 \geq5 Observed 7 18 25 17 12 5 Using $\alpha$ = 0.10, the critical value of chi-square for the data is _______.

(Multiple Choice)

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Question 20

Showing 1 - 20 of 85

A researcher is interested in using a chi-square test of independence to determine if age is independent of minutes spent reading.Age is divided into four categories while minutes spent reading is classified as high, medium, low.The number of degrees of freedom for this test is 12.

Use the following set of observed frequencies to test the independence of the two variables.Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. 12 10 8 20 24 26 Using $\alpha$ = 0.05, the critical chi-square value is _______.

When using the chi-square goodness-of-fit test, the type of distribution (uniform, Poisson, normal)being used does not influence the hypothesis test.

A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a uniform distribution for a dataset with "k" categories.This test has (k-3)degrees of freedom.

Anita Cruz recently assumed responsibility for a large investment portfolio.She wonders whether the industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks. Anita's null hypothesis is ______________.

A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution.There are 8 categories, and lambda must be estimated.Alpha is chosen to be 0.10.The critical (table)value of chi-square is _______.

A goodness of fit test is to be performed to see if consumers prefer any of three package designs (A, B, and C)more than the other two.A sample of 60 consumers is used.What is the expected frequency for category A?

A test of independence is to be performed.The contingency table has 4 rows and 5 columns.What would the degrees of freedom be?

A researcher believes that a variable is Poisson distributed across six categories.To test this, the following random sample of observations is collected: Categary 0 1 2 3 4 \geq5 Observed 7 18 25 17 12 5 Using $\alpha$ = 0.10, the critical value of chi-square for the data is _______.

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Probability

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Analysis of Variance and Design of Experiments

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Building Multiple Regression Models

Time-Series Forecasting and Index Numbers

Nonparametric Statistics

Statistical Quality Control

Decision Analysis

Filters

Exam 16: Analysis of Categorical Data

A researcher is interested in using a chi-square test of independence to determine if age is independent of minutes spent reading.Age is divided into four categories while minutes spent reading is classified as high, medium, low.The number of degrees of freedom for this test is 12.

Use the following set of observed frequencies to test the independence of the two variables.Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. 12 10 8 20 24 26 Using α\alphaα = 0.05, the critical chi-square value is _______.

When using the chi-square goodness-of-fit test, the type of distribution (uniform, Poisson, normal)being used does not influence the hypothesis test.

A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a uniform distribution for a dataset with "k" categories.This test has (k-3)degrees of freedom.

Anita Cruz recently assumed responsibility for a large investment portfolio.She wonders whether the industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks. Anita's null hypothesis is ______________.

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals. Using α\alphaα = .01, critical chi-square value is ______________.

A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution.There are 8 categories, and lambda must be estimated.Alpha is chosen to be 0.10.The critical (table)value of chi-square is _______.

A goodness of fit test is to be performed to see if consumers prefer any of three package designs (A, B, and C)more than the other two.A sample of 60 consumers is used.What is the expected frequency for category A?

A test of independence is to be performed.The contingency table has 4 rows and 5 columns.What would the degrees of freedom be?

A researcher believes that a variable is Poisson distributed across six categories.To test this, the following random sample of observations is collected: Categary 0 1 2 3 4 \geq5 Observed 7 18 25 17 12 5 Using α\alphaα = 0.10, the critical value of chi-square for the data is _______.

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Probability

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Analysis of Variance and Design of Experiments

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Building Multiple Regression Models

Time-Series Forecasting and Index Numbers

Nonparametric Statistics

Statistical Quality Control

Decision Analysis

Filters

Use the following set of observed frequencies to test the independence of the two variables.Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. 12 10 8 20 24 26 Using $\alpha$ = 0.05, the critical chi-square value is _______.

A researcher believes that a variable is Poisson distributed across six categories.To test this, the following random sample of observations is collected: Categary 0 1 2 3 4 \geq5 Observed 7 18 25 17 12 5 Using $\alpha$ = 0.10, the critical value of chi-square for the data is _______.