# Exercises - Chi Square Tests

1. A researcher wishes to see if the five ways (drinking decaffeinated beverages, taking a nap, going for a walk, eating a sugary snack, other) people use to combat midday drowsiness are equally distributed among office workers. A sample of 60 office workers is selected, and the following data are obtained. At .10 significance level can it be concluded that there is no preference? $$\begin{array}{l|c|c|c|c|c} \textrm{Method} & \textrm{beverage} & \textrm{nap} & \textrm{walk} & \textrm{snack} & \textrm{other}\\\hline \textrm{Number} & 21 & 16 & 10 & 8 & 5 \end{array}$$

2. Nationwide the shares of carbon emissions for the year 2000 are transportation, 33%; industry, 30%; residential, 20%; and commercial, 17%. A state hazardous materials official wants to see if her state is the same. Her study of 300 emissions sources finds transportation, 36%; industry, 31%; residential, 17%; and commercial, 16%. At a 0.05 significance level, can she claim the percentages are the same?

3. A study is conducted as to whether there is a relationship between joggers and the frequency of consumption of nutritional supplements. A random sample of 210 subjects is selected, and they are classified as shown. At a 0.05 significance level, test the claim that jogging and the consumption of supplements are not related. $$\begin{array}{lccc} & \textrm{Daily} & \textrm{Weekly} & \textrm{As Needed}\\\hline \textrm{Joggers} & 34 & 52 & 23\\ \textrm{Non-joggers} & 18 & 65 & 18 \end{array}$$

4. An advertising firm has decided to ask 92 customers at each of three local shopping malls if they are willing to take part in a market research survey. According to previous studies, 38% of Americans refuse to take part in such surveys. The results are shown here. At a 0.01 significance level, test the claim that the proportions of those who are willing to participate are equal.

$$\begin{array}{lccc} & \textrm{Mall A} & \textrm{Mall B} & \textrm{Mall C}\\\hline \textrm{Will Participate} & 52 & 45 & 36\\ \textrm{Will Not Participate} & 40 & 47 & 56\\ \end{array}$$

5. A researcher wishes to see if the proportions of workers for each type of job have changed during the last 10 years. A sample of 100 workers is selected, and the results are shown. At a 0.05 significance level, test the claim that the proportions have not changed.

$$\begin{array}{lcccc} & \textrm{Services} & \textrm{Manufacturing} & \textrm{Government} & \textrm{Other}\\\hline \textrm{10 years ago} & 33 & 13 & 11 & 3\\ \textrm{Now} & 18 & 12 & 8 & 2\\ \end{array}$$

6. Test the claim that births are uniformly distributed among the months (i.e., one twelfth of the number of births occur on average in any one month), using the following data collected over the course of one year.

$$\begin{array}{lr|lr} \textrm{Jan} & 34 & \textrm{Jul} & 36\\ \textrm{Feb} & 31 & \textrm{Aug} & 38\\ \textrm{Mar} & 35 & \textrm{Sep} & 37\\ \textrm{Apr} & 32 & \textrm{Oct} & 36\\ \textrm{May} & 35 & \textrm{Nov} & 35\\ \textrm{Jun} & 35 & \textrm{Dec} & 35\\ \end{array}$$

7. Based on the following data from the doomed voyage of the Titanic. decide if the chances that a randomly selected passenger survived was independent of their status.

$$\begin{array}{l|cccc|c} & \textrm{Crew} & \textrm{1st Class} & \textrm{2nd Class} & \textrm{3rd Class} & \textrm{Total} \\\hline \textrm{Lived} & 212 & 202 & 118 & 178 & 710\\ \textrm{Died} & 673 & 123 & 167 & 528 & 1491\\\hline \textrm{Total} & 885 & 325 & 285 & 706 & 2201\\ \end{array}$$

8. Decide if the proportions of Democrats, Republicans, and Independents are the same for both men and women, based on the following sample data. $$\begin{array}{l|ccc} & \textrm{Democrat} & \textrm{Republican} & \textrm{Independent}\\\hline \textrm{Male} & 36 & 45 & 24\\ \textrm{Female} & 48 & 33 & 16\\ \end{array}$$

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