Exam 16: Analysis of Categorical Data

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 recent national poll showed the reading habits of adults during the last 12 months: A poll in a small Midwestern town shows the following percentages: The observed chi-squared statistic is ______.

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

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles.The following is a contingency table from a random sample of 385 individuals: The researcher uses α = 0.05.The observed chi-square value is ______.

The decision rule in a chi-square goodness-of-fit test is to reject the null hypothesis if the computed chi-square is greater than the table chi-square.

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 alternative hypothesis 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 ______________.

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 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 critical chi-square value is _______.

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles.The following is a contingency table from a random sample of 385 individuals: The researcher uses α = 0.05.The number of degrees of freedom 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 _______.

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?

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

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?

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

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 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 estimate of the expected number of individuals with income less than $30,000 who purchase regular gasoline when income and type of gasoline are independent 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 _______.

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 ____.