Exam 16: Analysis of Categorical Data

A researcher believes that arrivals at a walk-in hair salon are Poisson distributed.The following data represent a distribution of frequency of arrivals in a one hour time period. Using $\alpha$ = 0.10,the critical chi-square value for this goodness-of-fit test is _______.

The null hypothesis in a chi-square goodness-of-fit test is that the observed distribution is the same as the expected distribution.

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. Anita's null hypothesis is ______________.

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals. The null hypothesis is ______________.

A suburban realtor is studying commuter time in the Houston metropolitan area.She has been told the average weekday travel time from a southern suburb at 8:00am is 45 minutes.For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00am.She expects the data are uniformly distributed across the five months.Her sample of observed data yields the following frequencies 9 days,15 days,8 days,11 days,12 days.Using $\alpha$ = .01,the appropriate decision 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 minus one.

In a chi-square goodness-of-fit test,actual frequencies are also called calculated frequencies.

A cancer research group surveys 100 women more than 40 years old to test the hypothesis that 50% of women in this age group have regularly scheduled mammograms.Forty of the women respond affirmatively.Using $\alpha$ = 0.05,the observed value of chi-square is __________.

Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),monitors the default rate on personal loans at the AFB 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,the appropriate decision is _______.

Contingency tables should not be used with expected cell frequencies _______.

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. The observed value of chi-square for this goodness-of-fit test is _____.

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 $\alpha$ = .05,critical chi-square value is ______________.

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,appropriate decision is ______________.

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 observed value of chi-square is ______________.

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 _______.

Ophelia O'Brien,VP of Consumer Credit of American First Banks (AFB),monitors the default rate on personal loans at the AFB 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 _______.

A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution.There are 6 categories,and lambda must be estimated.How many degrees of freedom should be used?