Two-Way Table Answers

Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college:
$\begin{array}{|ccc|}\hline & \text{Play chess}& \text{Don`t play chess}\\ \text{Male students}& 25& 162\\ \text{Female students}& 19& 148\\ \hline\end{array}$
Answer the following questions about the table. Be sure to show any calculations.
What question about the population of students at the state college would this table attempt to answer?
State $H^0$ and $H^1$ for the test related to this table.

How may a two-way table be used to examine potential relationships between two distinct categories within the same sample group?

Find the expected count and the contribution to the chi-square statistic for the (Group 1, No) cell in the two-way table below.

$\begin{array}{|cccc|}\hline & \text{Yes}& \text{No}& \text{Total}\\ \text{Group 1}& 56& 42& 98\\ \text{Group 2}& 135& 67& 202\\ \text{Group 3}& 66& 23& 89\\ \text{Total}& 257& 132& 389\\ \hline\end{array}$
Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.
Expected count =?
contribution to the chi-square statistic = ?

Is there a relationship between gender and relative finger length? To find out, we randomly selected 452 U.S. high school students who completed a survey. The two-way table summarizes the relationship between gender and which finger was longer on the left hand (index finger or ring finger)

. $\begin{array}{lc}& \text{Gender}\\ \text{Longer finger}& \begin{array}{lcrr}& \text{ Female }& \text{ Male }& \text{ Total }\\ \text{ Index finger }& 78& 45& 123\\ \text{ Ring finger }& 82& 152& 234\\ \text{ Same length }& 52& 43& 95\\ \text{ Total }& 212& 240& 452\end{array}\end{array}$

Suppose we randomly select one of the survey respondents. Define events R: ring finger longer and F: female. Find P(R|F). Interpret this value in context.

The following two-way contingency table gives the breakdown of the population of adults in a town according to their highest level of education and whether or not they regularly take vitamins:
$\begin{array}{|ccc|}\hline \text{Education}& \text{Use of vitamins takes}& \text{Does not take}\\ \text{No High School Diploma}& 0.03& 0.07\\ \text{High School Diploma}& 0.11& 0.39\\ \text{Undergraduate Degree}& 0.09& 0.27\\ \text{Graduate Degree}& 0.02& 0.02\\ \hline\end{array}$
You select a person at random. What is the probability the person does not take vitamins regularly?

The two-way table shows the results from a survey of dog and cat owners about whether their pet prefers dry food or wet food.
$\begin{array}{ccc}& \text{ Dry }& \text{ Wet }\\ \text{ Cats }& 10& 30\\ \text{ Dogs}& 20& 20\end{array}$
Does the two-way table show any difference in preferences between dogs and cats? Explain.

2,500 people were chosen at random for the sample, and when asked which season they preferred. Their responses, along with their age group, are summarized in the two-way table below. 
$\begin{array}{cccccc} & \text{Winter}& \text{Spring}& \text{Summer }& \text{Fall}& \text{Total}\\ \text{Children}& 30& 0& 170& 0& 200\\ \text{Teens}& 150& 75& 250& 25& 500\\ \text{Adults }& 250& 250& 250& 250& 1000\\ \text{Seniors}& 300& 150& 50& 300& 800\\ \text{Total}& 730& 475& 720& 575& 2500\end{array}$ 
Among those whose favorite season is spring, what proportion are adults? 
$a)\frac{250}{1000}$ 
$b)\frac{250}{2500}$ 
$c)\frac{475}{2500}$ 
$d)\frac{250}{475}$ 
$e)\frac{225}{475}$ 
 

The accompanying two-way table was constructed using data in the article “Television Viewing and Physical Fitness in Adults” (Research Quarterly for Exercise and Sport, 1990: 315–320). The author hoped to determine whether time spent watching television is associated with cardiovascular fitness. Subjects were asked about their television-viewing habits and were classified as physically fit if they scored in the excellent or very good category on a step test. We include MINITAB output from a chi-squared analysis. The four TV groups corresponded to different amounts of time per day spent watching TV (0, 1–2, 3–4, or 5 or more hours). The 168 individuals represented in the first column were those judged physically fit. Expected counts appear below observed counts, and MINITAB displays the contribution to $\left(x^2\right)$ from each cell.
State and test the appropriate hypotheses using $\alpha =0.05$
$\begin{array}{|cccc|}\hline & 1& 2& Total\\ 1& 35& 147& 182\\ & 25.48& 156.52& \\ 2& 101& 629& 730\\ & 102.20& 627.80& \\ 3& 28& 222& 250\\ & 35.00& 215.00& \\ 4& 4& 34& 38\\ & 5.32& 32.68& \\ Total& 168& 1032& 1200\\ \hline\end{array}$
$Chisq=3.557 + 0.579 + 0.014 + 0.002 + 1.400 + 0.228 + 0.328 + 0.053=6.161$
$df=3$