Exam 15: Chi-Squared Tests

Which statistical technique is appropriate when we compare two or more populations of qualitative data with two or more categories?

In a chi-squared test of a contingency table,the value of the test statistic was χ² = 15.652,and the critical value at α = .025 was 11.1433.Thus,we must reject the null hypothesis at α = .025.

How does a multinomial distribution differ from a binomial distribution?

Which test(s)can you use when you want to describe a population with two categories?

The total of the observed frequencies in a multinomial experiment must equal nk where n is the number of trials and k is the number of categories.

A chi-squared test is used to describe a population of nominal data.

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 large value of the chi-squared test statistic in a test of normality means you reject H₀ and conclude that the data ____________________ (do/do not)come from a normal distribution.

The human resources manager of a consumer product company asked a random sample of employees how they felt about the work they were doing.The following table gives a breakdown of their responses by whether the employee is part time or full time (aka work status).Do the data provide sufficient evidence to conclude that the level of job satisfaction is related to their work status? Use α = .10.

Which of the following statements regarding the chi-squared distribution is true?

A left-tailed area in the chi-squared distribution equals .10.For 5 degrees of freedom the table value equals 9.23635.

The number of degrees of freedom associated with the chi-squared test statistic for normality is the number of ____________________ minus 1 minus the number of ____________________ estimated.

To analyze the relationship between two nominal variables,which test(s)can you use?

If the expected frequency e_i for any cell i is less than 5,we should:

The null hypothesis states that the sample data came from a normally distributed population.The researcher calculates the sample mean and the sample standard deviation from the data.The data arrangement consisted of five categories.Using α = .05,the appropriate critical value for this chi-squared test for normality is 5.99147.

A chi-squared test of a contingency table with 6 degrees of freedom results in a test statistic of 13.25.Using the chi-squared table,the most accurate statement that can be made about the p-value for this test is that p-value is greater than .025 but smaller than .05.

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

When we test for differences between two populations of nominal data with two categories,we can use only one technique,namely,the chi-squared test of a contingency table.

Student Absenteeism Consider a multinomial experiment involving n = 200 students of a large high school.The attendance department recorded the number of students who were absent during the weekdays.The null hypothesis to be tested is: H₀: p₁ = .10,p₂ = .25,p₃ = .30,p₄ = .20,p₅ = .15. -{Student Absenteeism Narrative} Test the hypothesis at the 5% level of significance with the following frequencies: (n = 50)

If we use the chi-squared method of analysis we must first check that there are at least 5 observations in each cell of the contingency table.