AP Statistics: Inference for Categorical Data (Chi-Square) Practice Test

Y follows a chi-squared distribution with 6 degrees of freedom and X 1 through X n
are independent standard normal variables. , what is n?

Find the degrees of freedom.

What must be true about the expected values in a chi-square test?

Which test would you use to see if the distribution of music that Californians listen to is the same as that of Nevadans? 900 Californians and 600 Nevadans were surveyed

In 1974, each acre of the Tahoe basin was assessed to see what condition the soil was in. 23% of acres were of type I, 32% were of type II, 41% were of type III, and 16% were of type IV. This year the region was assessed again and the number of each type were again determined. Which test would you use?

What are the expected counts of a female who likes Pepsi?

A chi-square test is used to test whether a 0 to 9 spinner is “fair” (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be

Recent revenue shortfalls in a mid western state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results are in the table provided. Why hypotheses would be appropriate for performing a chi-square test?

A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race of the driver. The results are summarized in the table provided. The category that contributes the largest component to the χ2 statistic is

The proportion of this city’s population in each of the racial categories listed above is as follows:

We wish to test H 0 : The racial distribution of traffic tickets in the city is the same as the racial distribution of the city’s population.

Which statement is NOT correct about the chi-square test statistic?

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year. She wants to know if each type of food will be equally popular so she can start ordering supplies making other plans. To find out, she selects a random sample of 100 students and asks them, “Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?” Here are the data in the table provided. An appropriate null hypothesis to test whether the food choices are equally popular is:

Which of the following is false?

What are the degrees of freedom for the following χ2 test?

Tate works at an ice cream stand. Every customer can choose one of two toppings—sprinkles or chocolate chips. He recorded the age group and the chosen topping for a random sample of 120 customers. Here are the results: Tate wants to perform a χ2, squared test of independence between age and topping. What is the expected count for the cell corresponding to adults that chose sprinkles?

Edison, Xiu, and Amia are childhood friends who go to different high schools. They were wondering if there’s a difference between their schools in the number of friends people have on social media. They each surveyed a random sample of students from their schools, asking for the number of friends they have on social media. Here are the results: Tate wants to perform a χ2 test of homogeneity on these results. What is the expected count for the cell corresponding to students from Edison’s school that have more than 300 friends?

A market researcher for a communications company took a sample of 300 customers to see if those with children were more or less likely to pay for upgraded internet speeds. Here are the outcomes and partial results of a chi- square test (expected counts appear below observed counts):They want to use these results to carry out a  χ2 test of association. Assume that all conditions for inference were met. What are the values of the test statistic and P-value for their test?

A group of researchers wondered whether there was an association between handedness and which foot was longest. They took a random sample of people, measured their feet, and recorded their handedness. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts): They want to use these results to carry out a χ2 test of association. Assume that all conditions for inference were met. What are the values of the test statistic and P-value for their test?

A market researcher was curious about the colors of different types of vehicles. They obtained a random sample of 180 sedans and a separate random sample of 180 trucks. Here is a summary of the colors in each sample and the results from a chi-squared test: χ2 = 11.558, DF = 3, P-value = 0.009 Assume that all conditions for inference were met. At the α = 0.05 significance level, what is the most appropriate conclusion to draw from this test?

A company offers a smartphone in 3 different colors and 3 different capacities. A market researcher was curious if there was a relationship between the color and capacity that owners of this phone preferred. They obtained information about a random sample of 500 owners. Here is a summary of the data and the results from a chi-squared test:χ2 = 8.479, DF = 4, P-value = 0.076 Assume that all conditions for inference were met. At the α = 0.05 significance level, what is the most appropriate conclusion to draw from this test?