Exam 16: Analysis of Categorical Data

A gasoline distributor wonders whether an individual's income levels influences the grade of gasoline purchased. Using $\alpha$ = .05, the critical chi-square value 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?

Catherine Lee, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages.She wonders whether acceptance is influenced by children in the household.Her staff prepared the following contingency table from a random sample of 100 households: Using $\alpha$ = .05, the critical value of chi-square is ___.

The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated.

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'. Using $\alpha$ = 0.05, the observed chi-square value is ___.

Sami Wilson believes that number of cars arriving at his Spotless Car Wash follow a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis: The number of degrees of freedom for this goodness-of-fit test is ___.

In a chi-square test of independence the contingency table has 4 rows and 3 columns.The number of degrees of freedom for this test is 7.

A variable contains four categories.It is expected that data are uniformly distributed across these four categories.To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21.Using $\alpha$ = .05, the observed chi-square value is ___.

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 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 ___.

The senior executives of CareFree Insurance, Inc.feel that "a minority of our employees perceive an authoritarian management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis.Eighty employees rate the management as authoritarian.Using $\alpha$ = 0.05, the null hypothesis is ___.

Catherine Lee, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages.She wonders whether acceptance is influenced by children in the household.Her staff prepared the following contingency table from a random sample of 100 households: Using $\alpha$ = .05, the appropriate decision is ___.

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 26, 10, 17, 21, and 26.Using $\alpha$ = .01, the observed chi-square value is ___.

The senior executives of CareFree Insurance, Inc.feel that "a minority of our employees perceive an authoritarian management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis.Eighty employees rate the management as authoritarian.Using $\alpha$ = 0.05, the observed value of chi-square is ___.

A researcher believes that a variable is Poisson distributed across six categories.To test this, the following random sample of observations is collected: Using $\alpha$ = 0.10, the critical value of chi-square for the data is ___.

Sami Wilson believes that number of cars arriving at his Spotless Car Wash follow a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis: The observed value of chi-square for this goodness-of-fit test is ___.

Sam Kenny, Director of Media Research, is analyzing subscribers to the Life in the Rockies magazine.He wonders whether subscriptions are influenced by the head of household's employment classification.His staff prepared the following contingency table from a random sample of 300 households: The observed value of chi-square is ___.

A researcher believes that a variable is Poisson distributed across six categories.To test this, the following random sample of observations is collected: Using $\alpha$ = 0.10, the observed chi-square value for this goodness-of-fit test is ___.

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'. Using $\alpha$ = 0.05, the critical chi-square value is ___.

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 critical value of chi-square is ___.