Exam 15: Categorical Versus Categorical: Tests

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 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.

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 ___.

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 ___.

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 ___.

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 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?

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, critical 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 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 $\alpha$ =.10, the appropriate decision is ___.

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

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 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: The null hypothesis 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: The observed value of chi-square for this goodness-of-fit test 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 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: The null hypothesis 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, observed chi-square value is ___.

In a chi-square goodness-of-fit test, theoretical frequencies are also called expected frequencies.

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 critical chi-square value 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?

Is there a relationship between studying and passing final exams? Fifty students were surveyed about their activities leading to the statistics final exam. The students indicated whether they studied or partied and also whether they passed or failed the statistics final exam. The results are shown in the table below: At the 5% significance level, can it be concluded that final exam results are related to activities leading up to the exam?