Exam 15: Categorical Versus Categorical: Tests

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 number of degrees of freedom for this goodness-of-fit test is ___.

When using the chi-square goodness-of-fit test, the type of distribution (uniform, Poisson, normal) being used does not influence the hypothesis test.

A survey was conducted to determine the voting intentions of student in a large university. The percent of student who would definitely vote, likely vote, uncertain or will not vote are as follows: Suppose 500 students were asked their intentions and gave the following responses: At the 5% significance level, determine whether there is a significant difference in the voting intentions of students.

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

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

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, observed chi-square value is ___.

A suburban realtor is studying commuter time in the Calgary metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00 a.m. 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 8:00 a.m. 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 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 $\alpha$ = 0.05. The number of degrees of freedom 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 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 chi-square goodness-of-fit test to determine if the observed frequencies in seven categories are uniformly distributed has six degrees of freedom.

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 ___.

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 appropriate decision 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. Answer False

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 estimates of the expected frequency in row 1 (A) column 1 (C) when the two variables are independent 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 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 critical 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: The observed value of chi-square is ___.

A recent national poll showed the reading habits of adults during the last 12 months: A poll in a small Maritime town shows the following percentages: Comparing the critical and observed values of the goodness-of-fit chi-squared statistic and $\alpha$ = 0.05, the appropriate decision is ___.

A suburban realtor is studying commuter time in the Calgary metropolitan area. She has been told the average weekday travel time from a southern suburb at 8:00 a.m. 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 8:00 a.m. 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 ___.