Exam 16: Analysis of Categorical Data

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 ______________.

Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis. Categary 0 1 2 3 4 \geq5 Observed 5 15 17 12 10 8 The number of degrees of freedom for this goodness-of-fit test is _______.

Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis. Cars per 15-rrirute iriterval 0 1 2 3 4 \geq5 Observed frequency 5 15 17 12 10 8 Using $\alpha$ = 0.05, the appropriate decision for this goodness-of-fit test 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: 18-25 26-35 36-45 46+ Style - 1 125 87 50 12 Style -2 13 12 22 25 Style -3 6 6 12 15 The researcher uses $\alpha$ = 0.05.The critical chi-square value 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 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 _______.

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.

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, observed chi-square value is ______________.

In a college dining hall, students with a full meal plan can eat up to four meals each day.The kitchen is now thinking that the meal consumption may more closely resemble a uniform 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 appropriate decision for this goodness of fit test 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. Number of Customer Arivals 0 1 2 3 4 \geq5 Frequency 47 56 39 22 18 10 Using $\alpha$ = 0.10, the observed chi-square value for this goodness-of-fit test 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 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'. 12 10 8 20 24 26 Using $\alpha$ = 0.05, the observed chi-square value is _______.

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

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

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of alternative toothpaste packages.She wonders whether acceptance is influenced by the age of the 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 ______________.

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, 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 ______________.

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 recent national poll showed the reading habits of adults during the last 12 months: 3 or more botiss 5 2 boxks 27 1 hook 38 No books 30 A poll in a small Midwestern town shows the following percentages: 3 or more botiss 1 2 boxks 22 1 hook 39 No books 38 The null hypothesis is: ______.

A chi-square goodness-of-fit test to determine if the observed frequencies in ten categories are Poisson distributed has nine degrees of freedom.