Exam 10: Associations Between Categorical Variables

Use the following table to answer the question. The following table summarizes the outcomes of a study that researchers carried out to determine if females expressed a greater fear of flying than males. -How many categorical variables are summarized in the table?

Use the following information to answer the question. Bellei Extravecchio Balsamico Tradizionale is a very expensive brand of balsamic vinegar. A twelve ounce bottle typically costs two- hundred dollars or more. In a blind taste test, a group of food experts tasted three premium balsamic vinegars, with the most expensive one being Bellei Extravecchio Balsamico Tradizionale. When asked to pick the most expensive balsamic vinegar, 92 got it right and 76 got it wrong. -If this group were just guessing, how many people (out of 168)would be expected to guess correctly?

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.

The following table shows the results from a study to see if a home remedy salve for bee stings worked better than a placebo. Each participant was randomly assigned to receive the home remedy salve or a placebo ointment. "Improvement" means that there were no symptoms of pain after fifteen minutes. The alternative hypothesis is that the home remedy salve leads to improvement (in this case, no pain). The p- value for a one- tailed Fisher's Exact Test with these data is 0.500. Suppose the study had turned out differently, as in the following table. Would Fisher's Exact Test have led to a p- value larger or smaller than 0.500? Explain.

The table below shows the gender and the percentage of each gender that spent different amounts at a local toy store. The data was taken from a random sample of single shoppers collected over five consecutive Saturdays at the toy store. Choose the reason(s)why you cannot do a chi- square test with this data.

Suppose a study was conducted to see whether there is an association between marital status and breast cancer remission. The table below shows the results from the study. Assume all conditions for testing have been met. This was an observational study of randomly chosen patients who had received similar chemotherapy treatments. Test the hypothesis that marital status and remission from breast cancer are associated, using a significance level of 0.05. Choose the correct decision regarding the null hypothesis and conclusion. Refer to the computer output below.

Use the following information to answer the question. A dowsing rod is a "Y" or "L" shaped instrument that some believe can find ground water. Many dowsers today use a pair of simple L- shaped metal rods. One rod is held in each hand, with the short arm of the L held upright, and the long arm pointing forward. When something is found, the rods cross over one another making an "X" over the found object. Skeptics of dowsing conducted an experiment to see if dowsing rods could find ground water. Five identical 3 foot by 3 foot plots of land were sectioned off and a container of water was buried in one of the plots. Below is a summary of the experiment results and the output for the goodness- of- fit test. -Of the following statements, which one is not true about the chi- square statistic and p- value? Choose (d)if all statements are true.

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 a()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?

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 information to answer the question. The data in the top row of the table shows the number of vacation days taken by the respondent in the previous 90 days. The respondents also reported their level of happiness; Very H means very happy, and so on. -We wish to test whether happiness is associated with taking vacation days. Choose the statement that is true about the hypothesis test or choose (d)if all the statements are false.

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?

Use the following information to answer the question. The data in the top row of the table shows the number of vacation days taken by the respondent in the previous 90 days. The respondents also reported their level of happiness; Very H means very happy, and so on. -The following table shows the data after merging categories so that there are two column categories (0- 1 vacation days and 2 or more vacation days), and two row categories (happy and unhappy). Expected values for each cell are also shown in parentheses. Test the hypothesis that there is an association between happiness and number of vacation days taken in the last 90 days, using a significance level of 0.05. State the value of the test statistic rounded to two decimal places and state whether the p- value is closer to zero or one.

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.

Use the following table to answer the question. The following table summarizes the outcomes of a study that researchers carried out to determine if females expressed a greater fear of heights than males. -Find the expected number of men who should express a fear of heights, if the variables are independent. Round to the nearest whole number.

An eco- friendly home improvement store owner is thinking about carrying some new products and is interested in her customer's opinions. The shop owner decides to randomly sample 397 customers and ask them whether they have (a)heard about bricks made from recycled materials and (b)whether they have heard of landscaping materials made from recycled glass. She also asked each respondent how often they typically make purchases during a month. The table below shows the results from the study. Assume all conditions for testing have been met. Test the hypothesis that how the respondents answered the questions is associated with number of monthly purchases, using a significance level of 0.05. State the correct decision regarding the null hypothesis and write a conclusion using a full sentence. Refer to the output below.

The table below shows the gender and the percentage of each gender that spent different amounts at a local book store. The data was taken from a random sample of single shoppers collected over five consecutive Saturdays at the book store. Can a chi- square test be done with this data? Explain why or why not.

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

The following table shows the results from a study to see if a home remedy ointment for mosquito bites worked better than a placebo. Each participant was randomly assigned to receive the home remedy ointment or the placebo ointment. "Improvement" means there were no symptoms of itching after three minutes. The alternative hypothesis is that the home remedy ointment leads to improvement (in this case, less itching). The p- value for a one- tailed Fisher's exact test with these data is 0.618. Suppose the study had turned out differently, as in the following table. Would Fisher's Exact Test have led to a p- value larger or smaller than 0.618?

Use the following information to answer the question. A dowsing rod is a "Y" or "L" shaped instrument that some believe can find ground water. Many dowsers today use a pair of simple L- shaped metal rods. One rod is held in each hand, with the short arm of the L held upright, and the long arm pointing forward. When something is found, the rods cross over one another making an "X" over the found object. Skeptics of dowsing conducted an experiment to see if dowsing rods could find ground water. Five identical 3 foot by 3 foot plots of land were sectioned off and a container of water was buried in one of the plots. Below is a summary of the experiment results and the output for the goodness- of- fit test. -Choose the correct null and alternative hypothesis.

Find the expected number of women who should express a fear of flying, if the variables are independent. Round to the nearest whole number.