Exam 16: Analysis of Categorical Data

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 critical value of chi-square is ___.

A two-way table used for a test of independence is sometimes called a contingency table.

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 degrees of freedom for this test are ___.

In a chi-square goodness-of-fit test, theoretical frequencies are also called expected frequencies.

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.How many degrees of freedom should be used?

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. Using $\alpha$ = 0.05, the appropriate decision for this goodness-of-fit test is ___.

A gasoline distributor wonders whether an individual's income levels influences the grade of gasoline purchased. Using $\alpha$ = .05, the appropriate decision 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: Sam's null hypothesis 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 12.

Anita Gill recently assumed responsibility for a large investment portfolio.She wonders whether industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks: Using $\alpha$ = .01, the appropriate decision is ___.

A chi-square goodness-of-fit test to determine if the observed frequencies in ten categories are Poisson distributed has nine degrees of freedom.

A goodness-of-fit test is to be performed to see if web surfers prefer any of four websites (A, B, C, and D)more than the other three.A sample of 60 consumers is used.What is the expected frequency for website A?

A gasoline distributor wonders whether an individual's income levels influences the grade of gasoline purchased. Using $\alpha$ = .01, the observed chi-square value is ___.

Anita Gill recently assumed responsibility for a large investment portfolio.She wonders whether industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks: Using $\alpha$ = .01, the observed chi-square value is ___.

A contingency table is to be used to test for independence.There are 3 rows and 3 columns in the table.How many degrees of freedom are there for this problem?

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 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 chi-square value for this goodness-of-fit test is ___.

Ophelia McPhee, VP of Consumer Credit, Confederation First Bank (CFB), monitors the default rate on personal loans among CFB members.One of her standards is: "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans.Last Friday's sample contained 30 defaulted loans.Ophelia's null hypothesis is ___.

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 $\alpha$ = .10, the appropriate decision 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 appropriate decision is ___.