Exam 10: Associations Between Categorical Variables

The American Academy of Pediatrics recommends breast milk as the best nutrition for infants. A survey was conducted to see if pregnant women in their last trimester of pregnancy planned to breast feed their babies. It was thought that the income level of the women might be related to whether they planned to breast feed or not. The table below shows the results of the study: Assume that all conditions for testing have been met. This was an observational study of randomly selected pregnant women in their last trimester of pregnancy. Test whether there is an association between whether a woman plans to breast feed her baby or not and her income level, using a significance level of 0.05. Choose the correct decision and conclusion regarding the null hypothesis that no association exists. Refer to the computer output above.

Use the following information to answer questions (18) - (19). Bullying is a problem faced by many schools. To see if student perceptions of how well a high school is doing in dealing with bullying are related to class standing, a small survey was taken. Forty students were randomly selected from Central High School and asked their level of agreement to the following statement: "Central High School is doing a good job dealing with bullying in the school." The numbers in the parentheses are the expected values if "view on bullying" and "class standing" are independent. -Suppose we want to test to see if there is an association between class standing and view on bullying. Choose the statement that is true about the hypothesis test or choose (d) if all statements are false.

Choose the statement that is not true about the chi- square test or choose (d) if none of the statements is true.

Compare the sampling distributions of the normally distributed test statistic z and the chi-square test statistic. Specifically, how do the sampling distributions differ in shape and range of values?

In 2004, voters in the state of Michigan approved a constitutional amendment that banned same-sex marriage and civil unions in the state. To see if voter sentiment has changed over the years, a survey of 500 registered Michigan voters was taken. Each voter was asked his/her opinion on same-sex relationships with the following options: (a) same-sex marriage should be legalized, (b) same-sex unions should be legalized, (c) no same-sex relationships should be legalized, or (d) no opinion. Each voter was also classified by sex. If we wanted to test whether there was an association between the response to the question and sex, would this be a test of homogeneity or of independence?

Suppose a random sample of 1,220 U. S. adults were asked about their opinion regarding federal spending on infrastructure (i.e. roads and bridges). Respondents were asked whether federal spending on infrastructure was (a) too low, (b) adequate, or (c) too high. Respondents were classified by income level. If we wanted to test whether there was an association between the response to the question and income level, would this be a test of homogeneity or of independence?

Use the following table to answer questions (1) - (4). The following table summarizes the results of a study to determine if job satisfaction is related to pay category. -What fraction of salaried employees are satisfied with their jobs?

Test the hypothesis that the number of changes in racial classification is associated with students" racial classification in eighth grade, using a significance level of 0.05. Choose the correct decision regarding the null hypothesis and decision. Refer to the computer output above.

Suppose a random sample of 1,105 adults were asked about their opinion regarding salaries of full-time employees at a local state funded university. Respondents were asked whether salaries at the university were (a) too low, (b) adequate, or (c) too high. Respondents were also classified by income level. If we wanted to test whether there was an association between the response to the question and income level, would this be a test of homogeneity or of independence?

Use the following table to answer questions (1) - (4). The following table summarizes the results of a study to determine if job satisfaction is related to pay category. -The proportion of hourly employees is about 0.733. If the variables are independent, what is the expected number of hourly employees who are dissatisfied with their jobs.

Use the following information for following questions:. The roads in a particular state are in very poor condition, but the state claims that it does not have enough money to repair the roads. A proposal is on the ballot to raise the sales tax in the state from 6% to 7% to pay for repairing the roads. A month before the election, a survey of likely voters is taken. A random sample of 500 likely voters under the age of 30 is selected, a random sample of 500 likely voters aged 30-49 is selected, and a random sample of 500 likely voters aged 50 or more is selected. Each likely voter is asked whether he/she is in favor of the increase in the sales tax or not. -Choose the correct hypotheses to test whether there is an association between the response to whether to increase the sales tax or not and age.

Package design is important marketing tool, especially when marketing to children. The same food was presented to children using three different packaging designs. Each child was asked to select his or her favorite.In a taste test among 267 children, 68 selected package A as tasting best, 105 selected package B as tasting best, and 94 selected package C as tasting best. If there is no difference in the products in the 3 package designs, how many children out of the 267 would you expect to pick package B as tasting best?

Package design is an important marketing tool, especially when marketing to children. The same food was presented to children using three different packaging designs. Each child was asked to select his or her favorite. In a taste test among 243 children, 55 selected package A as tasting best, 112 selected package B as tasting best, and 76 selected package C as tasting best.If there is no difference in the products in the 3 package designs, how many children out of the 243 would you expect to pick package B as tasting best?

Suppose a researcher was interested in learning more about high school seniors' concerns about the future. The researcher asks the 750 randomly selected female high school seniors and the 800 randomly selected male high school seniors to rate their level of concern with the following statement: I am (a) not at all concerned (b) somewhat concerned or (c) very concerned about getting accepted into a two or four year college. If we wanted to test whether there was an association between the response to the question and the gender of the high school senior, would this be a test of homogeneity or independence?

Of the following statements, which one is true about the chi-square statistic and p-value? Choose (d) if all statements are true.