Exam 16: Analysis of Categorical Data

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 $\alpha$ = .10,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 27,30,29,21,and 24.Using $\alpha$ = .01,the degrees of freedom for this test are ___.

Catherine Chao,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 ___.

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?

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

Sami Schmitt believes that number of cars arriving at his Scrub and Shine 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 $\alpha$ = .01,the critical chi-square value is ___.

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 ___.

Sam Hill,Director of Media Research,is analyzing subscribers to the Life West of 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 ___.

Use the chi-square test of independence to perform contingency analysis.

Ophelia O'Brien,VP of Consumer Credit of Credit First Banks (CFB),monitors the default rate on personal loans at the CFB member banks.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.Using $\alpha$ = 0.01,critical chi-square value is ___.

Sami Schmitt believes that number of cars arriving at his Scrub and Shine 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 critical value of chi-square for this goodness-of-fit test 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 appropriate decision is ___.

The 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 ___.