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

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 appropriate decision 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 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 value of the observed chi-square for the data 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 researcher is interested in using a chi-square test of independence to determine if age is independent of minutes spent reading.Age is divided into four categories while minutes spent reading is classified as high,medium,low.The number of degrees of freedom for this test is 12.

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.Ophelia's null hypothesis 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 _______. A)9.236 B)1.064 B)7.779 C)13.277 D)12.89

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. Using $\alpha$ = .05,appropriate decision is ______________.

A travel agent believes that vacation destinations are independent of the region of the country that the vacationer resides.She has compiled a table with six vacation destinations and five regions throughout the United States.When applying a chi-square test of independence to this table,the number of degrees of freedom is _____.

Sam Hill,Director of Media Research,is analyzing subscribers to the TravelWorld magazine.He wonders whether subscriptions are influenced by the head of household's highest degree earned.His staff prepared the following contingency table from a random sample of 300 households. Sam's null hypothesis is ______________.

A market researcher is studying the use of coupons by consumers of varying ages.She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out.It is expected that data are uniformly distributed across the four age categories.The observed data results in frequencies of 22,35,32,and 21.Using $\alpha$ = .10,the appropriate decision is _______.

Sam Hill,Director of Media Research,is analyzing subscribers to the TravelWorld magazine.He wonders whether subscriptions are influenced by the head of household's highest degree earned.His staff prepared the following contingency table from a random sample of 300 households. The observed value of chi-square is ______________.

A market researcher is studying the use of coupons by consumers of varying ages.She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out.It is expected that data are uniformly distributed across the four age categories.The observed data results in frequencies of 22,35,32,and 21.Using $\alpha$ = .05,the appropriate decision 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 that 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 observed chi-square value is _______.

A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a uniform distribution for a dataset with "k" categories.This test has (k-3)degrees of freedom.

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 ______________.

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 level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals. Using $\alpha$ = .01,observed chi-square value 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. Using $\alpha$ = .05,critical chi-square value is ______________.