AP Statistics Inference for Categorical Data

What is the branch of mathematics dealing with the collection, organization, analysis, interpretation and presentation of data?

• Algebra

• Geometry

• Probability

• Statistics

A random sample of 100 people from Country S had 15 people with blue eyes. A separate random sample of 100 people from Country B had 25 people with blue eyes. Assuming all conditions are met, which of the following is a 95 percent confidence interval to estimate the difference in population proportions of people with blue eyes (Country S minus Country B) ?

• (-0.01, 0.21)

• (-0.15,-0.05)

• (-0.19,-0.01)

• (-0.21, 0.01)

• (-0.24,0.04)

A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in Colorado. To estimate the difference between the proportions of deer with chronic wasting disease in two different regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region. The biologist checked for the following (see pic). Which of the following conditions for inference was the biologist checking?

• The population of deer within each region is approximately normal.

• It is reasonable to generalize from the samples to the populations.

• The samples are independent of each other.

• The observations within each sample are close to independent.

• The sampling distribution of the difference in sample proportions is approximately normal.

A state political analyst wanted to see whether there is an association between the region where a person lives and whether the person is in favor of increasing the state gas tax. A random sample of 270 state residents was selected, and the table below shows the results of the survey. Which of the following is closest to the -value of the appropriate test to investigate whether there is an association between the region where a person lives and whether the person is in favor of increasing the state gas tax, and what is the correct decision?

• 0.0644, we reject the null hypothesis

• 0.3596, we reject the null hypothesis

• 0.0644, we fail to reject the null hypothesis

• 0.3596, we fail to reject the null hypothesis

What happens to the shape of the chi-square distribution as the degrees of freedom increase?

• Nothing.

• Eventually it will go from being right-skewed to normal.

• Eventually it will go from being right-skewed to left-skewed.

• It's peak will increase, becoming more right-skewed.

A random sample of 240 adults over the age of 40 found that 144 would use an online dating service. Another random sample of 234 adults age 40 and under showed that 131 would use an online dating service. Assuming all conditions are met, which of the following is the standard error for a 90 percent confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service?

A study reports that 75 percent of young adults in a county get their news from online sources. A sociologist

believes that the percentage is actually greater than 75 percent. The sociologist will select a random sample of

young adults from around the county to interview. Which of the following is the most appropriate method for

investigating the sociologist’s belief?

• A one-sample -test for a difference in population proportions

• A one-sample -test for a sample proportion

• A one-sample -test for a population proportion

• A two-sample -test for a difference in population proportions

• A two-sample -test for a difference in sample proportions

A study was conducted to investigate whether there are regional differences in peanut butter preference in the United States. The country was divided into 7 geographic regions, and in each region a random sample of peanut butter eaters were asked whether they preferred creamy or crunchy peanut butter. The responses were summarized in a 7-by-2 table of counts for each combination of geographic region and creamy or crunchy peanut butter preference. Which of the following tests is the most appropriate for the investigation?

• A two-sample -test for a difference between means

• A two-sample -test for a difference between proportions

• A chi-square test of homogeneity

• A chi-square test of independence

• A chi-square goodness-of-fit test

The campus bookstore at a local university is interested in finding out whether the textbook preference and the class level (freshman, sophomore, junior, senior) of the student are associated. A random sample of 100 students is obtained, and each student in the sample is asked which textbook he or she prefers: new books, used books, or digital books. The students are also asked whether their class level is freshman, sophomore, junior, or senior. Which of the following is the appropriate test for the investigation?

• A one-sample -test for a population mean

• A two-sample -test for a difference between mea

• A chi-square goodness-of-fit test

• A chi-square test of homogeneity

• A chi-square test of independence

What types of data can be described by a frequency distribution?

• Categorical

• Quantitative