Exam 10: Associations Between Categorical Variables

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. Choose the correct hypotheses to test whether there is an association between the response to the question and income level.

Recently, many states have been considering legalizing the use of marijuana. A survey was taken last year where adults in one state were asked if they favored legalizing the use of marijuana. The following table displays the percentage of adults in the state who favor and who do not favor the legalization of marijuana for both males and females: Choose the reason(s) why you cannot perform a chi-square test on the data.

Genetically modified food has generated much controversy as to whether it is safe for humans to consume. A recent study was conducted to see if age is related to how a person views genetically modified food. The results appear in the following table: The alternative hypothesis is that age and view on genetically modified foods are associated. The p- value for Fisher's Exact Test with these data is 0.1748. Suppose the study had turned out differently, as in the following table. Would the p-value for Fisher's Exact Test be larger or smaller than 0.1748?

Choose the statement that is not true about Fisher's Exact Test or choose (d) if all the statements are true.

Typically the percentage of women in an engineering class at a particular university has been 15%. A new recruiting plan was implemented in the past year to increase the proportion of women in the incoming class. This year, there were 49 women and 208 men in the incoming class. The data are summarized below. Calculate the observed value of the chi-square statistic. Round to the nearest hundredth.

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

In many pharmaceutical studies, about 16% of all adult volunteers who take placebos (but who are told they have taken a cold remedy) reported that they suffered side effects of drowsiness, stomach upset, or headaches. A study was run on 250 children aged 8 to 12 to see if the results for children differ from those for adults. Below is a summary of the experiment conducted with 250 children aged 8 to 12 and the output for the goodness-of-fit test. Choose the correct null and alternative hypotheses.

Use the following information for following questions:. Almas caviar is a very expensive Iranian brand of Beluga sturgeon caviar. A one pound gold-plated tin typically costs $12,000 or more. In a blind taste test, a group of food experts tasted four premium Beluga sturgeon caviars, with the most expensive one being Almas caviar. When asked to pick the most expensive caviar, 141 got it right and 79 got it wrong. -Calculate the observed value of the chi-square statistic to test whether the proportion of people selecting the correct brand as most expensive differs from chance. Show all your work. Round to the nearest hundredth.

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. State the correct hypothesis to test whether there is an association between the response to the questions and income level.

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 represents the fraction of people in the study who were satisfied 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. -If we want to test whether there is an association between the response to the tax increase and age, would this be a test of homogeneity or of independence?

Use the following information for following questions:. Almas caviar is a very expensive Iranian brand of Beluga sturgeon caviar. A one pound gold-plated tin typically costs $12,000 or more. In a blind taste test, a group of food experts tasted four premium Beluga sturgeon caviars, with the most expensive one being Almas caviar. When asked to pick the most expensive caviar, 141 got it right and 79 got it wrong. -If this group were just guessing, how many people (out of 220) would be expected to guess correctly?

A traffic study found that of 676 automobiles entering a busy intersection during the period from 6 A.M. to 9 A.M., 257 turned left, 221 turned right, and 198 drove straight through the intersection. Below is a summary of the data and the output for the goodness-of-fit test. Test the hypothesis that the traffic is not equally divided among the three directions. Using a goodness-of-fit test and a 0.05 level of significance, choose the correct decision regarding the null hypothesis and conclusion statement.

Choose the statement that is not true about the chi-square test or choose (d) if all the statements are true.

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. -How many categorical variables are summarized in the table?

Suppose a researcher was interested in learning more about parents' concerns when their children start elementary school. The researcher asks the parents of 800 randomly selected first graders in rural school district and the parents of 950 randomly selected first graders in an urban school district to rate their level of concern with the following statement: We are (a) not at all concerned (b) somewhat concerned or (c) very concerned about the nutrition level of school lunches. If we wanted to test whether there was an association between the response to the question and the type of school district that the first grader was attending, would this be a test of homogeneity or of independence?

Describe at least one advantage and one disadvantage of combining categories as was done in the previous question.

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 the cells in the above table are collapsed so that the new table is as follows: Expected values for each of the new cells are listed in the table in parentheses. Compute the value of the chi-square test statistic rounded to 2 decimal places.

Choose the statement about Fisher's Exact Test that is true or choose (d) if none of the statements is true.

Suppose a goodness-of-fit test is used to test the claim that obesity rates in the elderly have changed since the time of the Egyptian mummies. The p-value is calculated to be 0.00023. Describe the value of the chi-square test statistic (is it likely to be large? small?) and the decision regarding the null hypothesis that there is no difference in obesity rates for mummies and modern-day elderly people.