Exam 16: Analysis of Categorical Data

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

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 researcher believes that a variable is Poisson distributed across six categories.To test this, the following random sample of observations is collected: Categary 0 1 2 3 4 \geq5 Observed 7 18 25 17 12 5 Using $\alpha$ = 0.10, the value of the observed chi-square for the data is _______.

The null hypothesis for a chi-square test of independence is that the two variables are not related.

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

The manager of a grocery store believes that the number of people waiting in the express check out lane follows a Poisson distribution.While watching the lane at random times throughout the day and week, she collects the following information. People waiting in express check out lane 0 1 2 3 4 \geq5 Observed frequency 35 41 22 14 3 2 The observed value of chi-square for this goodness-of-fit test is closest to_______.

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 _______.

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

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

In a college dining hall, students with a full meal plan can eat up to four meals each day.The kitchen would like to know the distribution of meal consumption by students and think it would follow a Poisson distribution.Reviewing dining hall data over the past week, the following information is compiled. Meals 0 1 2 3 \geq4 Observed frequency 287 581 447 290 185 The observed value of chi-square for this goodness-of-fit test is closest to _______.

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 _______.

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 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 observed chi-square value 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.

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'. 12 10 8 20 24 26 Using $\alpha$ = 0.05, the estimates of the expected frequency in row 1 (A)column 1 (C)when the two variables are independent is _______.

The manager of a grocery store believes that the number of people waiting in the express check out lane follows a Poisson distribution.While watching the lane at random times throughout the day and week, she collects the following information. People waiting in express check out lane 0 1 2 3 4 \geq5 Observed frequency 35 41 22 14 3 2 Using $\alpha$ =0.10, the appropriate decision for this goodness of fit test is _______.

In a college dining hall, students with a full meal plan can eat up to four meals each day.The kitchen would like to know the distribution of meal consumption by students and think it would follow a Poisson distribution.Reviewing dining hall data over the past week, the following information is compiled. Meals 0 1 2 3 \geq4 Observed frequency 287 581 447 290 185 Using $\alpha$ =0.05, the critical value of chi-square for this goodness of fit test is _______.

The type of data most appropriate for use in the chi-square test of independence is ______.

A market researcher believes that industry type is independent of the operating margin.He compiles a table with seven industry classifications and classifies operating margin into five levels.When applying a chi-square test of independence to this table, the number of degrees of freedom is _____.