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Chapter 11: Q. 57 (page 758)
Which of the following is the correct number of degrees of freedom for the chi-square test using these data?
a.
b.
c.
d.
e.
Option (a) The degrees of freedom for the chi-square test for this two-way table are .
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Video games To determine if there is a relationship between age and playing video games, the Pew Research Center asked randomly selected adults for their age and if they “ever play video games on a computer, TV, game console, or portable device like a cell phone.” Here is a two-way table summarizing the results of the study:
a. Construct a segmented bar graph to display the relationship between age group and response to the question about video games.
b. Describe the association shown in the segmented bar graph in part (a).
Is astrology scientific? The General Social Survey (GSS) asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of counts for people in the sample who had three levels of higher education:
a. State appropriate hypotheses for performing a chi-square test for independence in this setting.
b. Compute the expected counts assuming that is true.
c. Calculate the chi-square test statistic, df, and P-value.
d. What conclusion would you draw?
The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of students and asks them, “Which type of food do you prefer: Ramen, tacos, pizza, or hamburgers?” Here are her data:
The P-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion at a significance level of 0.05?
a. Because is less than reject . There is convincing evidence that the food choices are equally popular.
b. Because is less than reject There is not convincing
evidence that the food choices are equally popular.
c. Because is less than reject . There is convincing evidence that the food choices are not equally popular.
d. Because is less than fail to reject There is not convincing evidence that the food choices are equally popular.
e. Because is less than fail to reject There is convincing
evidence that the food choices are equally popular.
Online banking A recent poll conducted by the Pew Research Center asked a random sample of Internet users if they do any of their banking online. The table summarizes their responses by age. Is there convincing evidence of an association between age and use of online banking for Internet users?
Aw, nuts! Refer to Exercise 1.
a. Confirm that the expected counts are large enough to use a chi-square distribution to calculate the P-value. What degrees of freedom should you use?
b. Use Table C to find the P-value. Then use your calculator’s χ2 cdf command.
c. What conclusion would you draw about the company’s claimed distribution for its deluxe mixed nuts?
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