The number of cars sold by three salespersons over a 3-month period are shown below: \[\begin{array} { | l | c | c | c | } \hline & { \text { Brand of Car } } \\ \hline \text { Salesperson } & \text { Brand A } & \text { Brand B } & \text { Brand C } \\ \hline \text { David } & 7 & 2 & 6 \\ \hline \text { Edward } & 11 & 4 & 8 \\ \hline \text { Frank } & 8 & 5 & 3 \\ \hline \end{array}\] Using the 5% level of significance, test for the independence of salesperson and type of product sold.

@#IMG-DLM& The two variables (salesperson and bran

A study of education levels of 500 voters and their political party affiliations in a particular state in Australia showed the following results. \[\begin{array} { | l | c | c | c | } \hline & { \text { Party Affliation } } \\ \hline \text { Education level completed } & \text { Liberal } & \text { Other } & \text { Labour } \\ \hline \text { Frimary education } & 40 & 20 & 80 \\ \hline \text { Secondary education } & 70 & 30 & 60 \\ \hline \text { Tertiary education } & 90 & 50 & 60 \\ \hline \end{array}\] Is education level independent of political affiliation? Test at the 5% level of significance.

H 0 : Party affiliation and Education level

Exam 14: Additional Tests for Nominal Data: Chi-Squared Tests

Last year, Brand A mobile android phones had 45% of the market, Brand B had 35% and Brand C had 20%. This year the makers of Brand C launched a heavy advertising campaign. A random sample of mobile phone stores shows that of the 10,000 android mobile phones sold, 4350 were Brand A, 3450 were Brand B, and 2200 were Brand C.Has the market changed? Test at $\alpha =$ 0.05.

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Question 1

Correct Answer:

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$H _ { 0 } : p _ { 1 } = 0.45$ , $p _ { 2 } = 0.35,$ $p _ { 3 } = 0.20$ .
H_A: At least two proportions differ from their specified values.
Rejection region: 2 > χ20.05, 2 = 5.99 or if p-value < α = 0.05.
Test statistic: $x ^ { 2 } =$ 25.714. p-value = 0.
Conclusion: Reject Ho accept HA at α of 5% and conclude that there is significant evidence that the market for android mobile phones has changed.

A large carpet store wishes to determine if the brand of carpet purchased is related to the purchaser's family income. As a sampling frame, they mailed a survey to people who have a store credit card. Five hundred customers returned the survey and the results follow: \multicolumn 3 |c| Brand of Carpet Family income Brand A Brand B Brand C High income 65 32 32 Middle income 80 68 104 Low income 25 35 59 At the 5% level of significance, can you conclude that the brand of carpet purchased is related to the purchaser's family income?

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Question 2

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$H _ { 0 } :$ The two variables (family income and brand of carpet) are independent.
H_A: The two variables are dependent.
Rejection region: $\chi ^ { 2 } > \chi _ { 0.05,4 } ^ { 2 } =$ 9.488.
Test statistic: $x ^ { 2 } =$ 27.372. p-value = 0.0.
Conclusion: Reject the null hypothesis. Yes.

The president of a large university has been studying the relationship between male/female supervisory structures in his institution and the level of employees' job satisfaction. The results of a recent survey are shown in the table below. Conduct a test at the 5% significance level to determine whether the level of job satisfaction depends on the boss/employee gender relationship. Boss/Employee Level of Satisfaction Male/Female Female/Male Male/Male Female/Female Satisfied 60 15 50 15 Neutral 27 45 48 50 Dissatisfied 13 32 12 55

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Question 3

Correct Answer:

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$H _ { 0 } :$ The two variables are independent.
H_A: The two variables are dependent.
Rejection region: $\chi ^ { 2 } > \chi _ { 0.05,6 } ^ { 2 } =$ 12.592.
Test statistic: $x ^ { 2 } =$ 92.709.
p-value = 0.0.
Conclusion: Reject the null hypothesis. Yes.

Which of the following may be used for hypothesis tests of nominal (categorical) data?

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Question 4

Which of the following statements is true for the chi-squared tests?

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Question 5

At present in Australia, voting in a Federal election is compulsory for all citizens 18 years or over. There has been some discussion to have this changed from being compulsory to voluntary. A study was done to investigate whether there was a relationship between gender and attitude towards changing voting in Australia from compulsory to voluntary. Participants were asked "Do you agree to change voting in Australian Federal Elections from compulsory to voluntary? A table of results from the sample is given below. At the 1% level of significance, is there a relationship between gender and attitude towards voluntary voting? Agreed Disagreed Undecided Female 15 25 30 Male 25 20 25

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Question 6

In a chi-squared test of a contingency table, the value of the test statistic was $\chi ^ { 2 } = 12.678$ , the significance level was ? = 0.05 and the degrees of freedom was 6. Thus:

(Multiple Choice)

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Question 7

Which of the following best describes the rejection region in a chi-squared test of independence?

(Multiple Choice)

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Question 8

The chi-squared test of a contingency table is based upon:

(Multiple Choice)

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Question 9

In chi-squared tests, the conventional and conservative rule - known as the rule of five - is to require that difference between the observed and expected frequency for each cell be at least 5.

(True/False)

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Question 10

The number of degrees of freedom associated with the chi-squared test for normality is the number of intervals used minus the number of parameters estimated from the data.

(True/False)

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Question 11

A chi-squared test of a contingency table with 4 rows and 4 columns shows that the value of the test statistic is 23. Which of the following best describes the p-value for this test?

(Multiple Choice)

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Question 12

The rule of five is used to ensure that the discrete distribution of the test statistic can be approximated by the continuous Chi-squared distribution.

(True/False)

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Question 13

To determine the critical values in the chi-squared distribution table, the process requires which of the following information?

(Multiple Choice)

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Question 14

In 2003, computers of Brand A controlled 25% of the market, Brand B 20%, Brand C 10% and Brand D 45%. In 2004, sample data were collected from many randomly selected stores throughout the country. Of the 1200 computers sold, 280 were Brand A, 270 were Brand B, 90 were Brand C and 560 were Brand D.Has the market changed since 2003? Test at the 1% significance level.

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Question 15

Which statistical technique is appropriate when we describe a single population of nominal data with exactly two categories?

(Multiple Choice)

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Question 16

The number of cars sold by three salespersons over a 3-month period are shown below: Brand of Car Salesperson Brand A Brand B Brand C David 7 2 6 Edward 11 4 8 Frank 8 5 3 Using the 5% level of significance, test for the independence of salesperson and type of product sold.

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Question 17

Which of the following statements is not correct?

(Multiple Choice)

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Question 18

A study of education levels of 500 voters and their political party affiliations in a particular state in Australia showed the following results. Party Affliation Education level completed Liberal Other Labour Frimary education 40 20 80 Secondary education 70 30 60 Tertiary education 90 50 60 Is education level independent of political affiliation? Test at the 5% level of significance.

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Question 19

When doing a Chi-squared goodness of fit test, we use Ho: The data are not normally distributed.

(True/False)

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Question 20

Which of the following may be used for hypothesis tests of nominal (categorical) data?

Which of the following statements is true for the chi-squared tests?

In a chi-squared test of a contingency table, the value of the test statistic was $\chi ^ { 2 } = 12.678$ , the significance level was ? = 0.05 and the degrees of freedom was 6. Thus:

Which of the following best describes the rejection region in a chi-squared test of independence?

The chi-squared test of a contingency table is based upon:

In chi-squared tests, the conventional and conservative rule - known as the rule of five - is to require that difference between the observed and expected frequency for each cell be at least 5.

The number of degrees of freedom associated with the chi-squared test for normality is the number of intervals used minus the number of parameters estimated from the data.

A chi-squared test of a contingency table with 4 rows and 4 columns shows that the value of the test statistic is 23. Which of the following best describes the p-value for this test?

The rule of five is used to ensure that the discrete distribution of the test statistic can be approximated by the continuous Chi-squared distribution.

To determine the critical values in the chi-squared distribution table, the process requires which of the following information?

Which statistical technique is appropriate when we describe a single population of nominal data with exactly two categories?

The number of cars sold by three salespersons over a 3-month period are shown below: Brand of Car Salesperson Brand A Brand B Brand C David 7 2 6 Edward 11 4 8 Frank 8 5 3 Using the 5% level of significance, test for the independence of salesperson and type of product sold.

Which of the following statements is not correct?

When doing a Chi-squared goodness of fit test, we use Ho: The data are not normally distributed.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 14: Additional Tests for Nominal Data: Chi-Squared Tests

Which of the following may be used for hypothesis tests of nominal (categorical) data?

Which of the following statements is true for the chi-squared tests?

In a chi-squared test of a contingency table, the value of the test statistic was χ2=12.678\chi ^ { 2 } = 12.678χ2=12.678 , the significance level was ? = 0.05 and the degrees of freedom was 6. Thus:

Which of the following best describes the rejection region in a chi-squared test of independence?

The chi-squared test of a contingency table is based upon:

In chi-squared tests, the conventional and conservative rule - known as the rule of five - is to require that difference between the observed and expected frequency for each cell be at least 5.

The number of degrees of freedom associated with the chi-squared test for normality is the number of intervals used minus the number of parameters estimated from the data.

A chi-squared test of a contingency table with 4 rows and 4 columns shows that the value of the test statistic is 23. Which of the following best describes the p-value for this test?

The rule of five is used to ensure that the discrete distribution of the test statistic can be approximated by the continuous Chi-squared distribution.

To determine the critical values in the chi-squared distribution table, the process requires which of the following information?

Which statistical technique is appropriate when we describe a single population of nominal data with exactly two categories?

The number of cars sold by three salespersons over a 3-month period are shown below: Brand of Car Salesperson Brand A Brand B Brand C David 7 2 6 Edward 11 4 8 Frank 8 5 3 Using the 5% level of significance, test for the independence of salesperson and type of product sold.

Which of the following statements is not correct?

When doing a Chi-squared goodness of fit test, we use Ho: The data are not normally distributed.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

In a chi-squared test of a contingency table, the value of the test statistic was $\chi ^ { 2 } = 12.678$ , the significance level was ? = 0.05 and the degrees of freedom was 6. Thus: