Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their c

Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their c

Question
Two-way tables
asked 2021-01-28

Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college:
\(\begin{array}{|c|c|c|}\hline&\text{Play chess}&\text{Don`t play chess}\\\hline \text{Male students} &25&162\\ \hline \text{Female students}&19&148 \\ \hline \end{array}\\\)
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.

Answers (1)

2021-01-29

Step 1: Information from the table
We have given that the two-way table from a sample of randomly selected students at their college. From the table, we can see that there are two attributes. one is gender (Male and female students) and other is choice (Play chess and don't play choice). So, one can ask a question that whether the two attribute dependent or not. It means whether there is a relationship between gender and choice.
Step 2: Formation of \(H^0\) and \(H^1\)
It is clear that the given table is a contingency table of 2 variable (attribute). So, in order to test the relationship between these one can apply chi-square independence of attribute test. In this case, we can define
\(H^0\): There is no dependency on the choice of play chess and gender
\(H^1\): There is the dependency of choice of play chess and gender

0

Relevant Questions

asked 2020-12-09

A random sample of 88 U.S. 11th- and 12th-graders was selected. The two-way table summarizes the gender of the students and their response to the question "Do you have allergies?" Suppose we choose a student from this group at random.

\(\begin{array}{c|cc|c} & \text { Female } & \text { Male } & \text { Total } \\ \hline \text{ Yes } & 19 & 15 & 34 \\ \text{ No } & 24 & 30 & 54 \\ \hline \text{ Total } & 43 & 45 & 88\\ \end{array}\)
What is the probability that the student is female or has allergies?
\((a)\frac{19}{88}\)
(b)\(\frac{39}{88}\)
(c)\(\frac{58}{88}\)
(d)\(\frac{77}{88}\)

asked 2020-11-09

The two-way table summarizes data on the gender and eye color of students in a college statistics class. Imagine choosing a student from the class at random. Define event A: student is male and event B: student has blue eyes.
\(\begin{array}{c|cc|c} &\text{Male}&\text{Female}&\text{Total}\\ \hline \text{Blue}&&&10\\ \text{Brown}&&&40\\ \hline \text{Total}&20&30&50 \end{array}\)
Copy and complete the two-way table so that events A and B are mutually exclusive.

asked 2020-12-03

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.
\(\begin{array}{c|c|c} &\text { Dry } & \text { Wet }\\ \hline \text{ Cats } & 10&30 \\ \hline \text{ Dogs} & 20&20\\ \end{array}\)
Does the two-way table show any difference in preferences between dogs and cats? Explain.

asked 2020-12-29

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:
\(\begin{array}{|c|c|c|c|c|} \hline \text {Education}& \text {Use of vitamins takes} &\text{Does not take}\\ \hline \text {No High School Diploma} & 0.03 & 0.07 \\ \hline \text{High School Diploma} & 0.11 & 0.39 \\ \hline \text {Undergraduate Degree} & 0.09 & 0.27 \\ \hline \text {Graduate Degree} & 0.02 & 0.02 \\ \hline \end{array}\)
You select a person at random. What is the probability the person does not take vitamins regularly?

asked 2020-10-20

Bayes' Theorem is given by \(P(A|B) = \frac{P(B|A) \cdot P(A)} {P(B)}\). Use a two-way table to write an example of Bayes' Theorem.

asked 2021-01-05

A study among the Piria Indians of Arizona investigated the relationship between a mother's diabetic status and the number of birth defects in her children. The results appear in the two-way table. \(\text{Diabetic status}\ \begin{array}{ll|c|c|c} && \text { Nondiabetic } & \text { Prediabetic } & \text { Diabetic } \\ \hline & \text { None } & 754 & 362 & 38 \\ \hline & \text { One or more } & 31 & 13 & 9 \end{array}\)

What proportion of the women in this study had a child with one or more birth defects?

asked 2021-01-08

The two-way table below describes the members of the U.S Senate in a recent year.
\(\begin{array}{ccc} \hline &\text{Male}&\text{Female}\\ \text{Democrats}&47&13\\ \text{Republicans}&36&4\\ \hline \end{array}\)
If we select a U.S. senator at random, what's the probability that the senator is a Democrat?

asked 2021-01-25

A survey of 4826 randomly selected young adults (aged 19 to 25 ) asked, "What do you think are the chances you will have much more than a middle-class income at age 30?" The two-way table summarizes the responses. \(\begin{array} {lc} & \text{Gender} \ \text {Opinion} & \begin{array}{l|c|c|c} & Female & Male & Total \\ \hline \text{Almost no chance} & 96 & 98 & 194 \\ \hline \begin{array}{l} \text{Some chance but} \\ \text{probably not} \end{array} & 426 & 286 & 712 \\ \hline A\ 50-50\ chance & 696 & 720 & 1416 \\ \hline \text{A good chance} & 663 & 758 & 1421 \\ \hline \text{Almost certain} & 486 & 597 & 1083 \\ \hline Total & 2367 & 2459 & 4826 \end{array}\ \end{array}\)

Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Find P(G | M). Interpret this value in context.

asked 2020-11-23

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 \(\displaystyle{x}^{{{2}}}\) from each cell.
State and test the appropriate hypotheses using \(\displaystyle\alpha={0.05}\)
\(\begin{array}{|c|c|}\hline & 1 & 2 & Total \\ \hline 1 & 35 & 147 & 182 \\ \hline & 25.48 & 156.52 & \\ \hline 2 & 101 & 629 & 730 \\ \hline & 102.20 & 627.80 & \\ \hline 3 & 28 & 222 & 250 \\ \hline & 35.00 & 215.00 & \\ \hline 4 & 4 & 34 & 38 \\ \hline & 5.32 & 32.68 & \\ \hline Total & 168 & 1032 & 1200 \\ \hline \end{array}\)
\(Chisq= 3.557\ +\ 0.579\ +\ 0.014\ +\ 0.002\ +\ 1.400\ +\ 0.228\ +\ 0.328\ +\ 0.053=6.161\)
\(\displaystyle{d}{f}={3}\)

asked 2021-01-19

Using data from the 2000 census, a random sample of 348 U.S. residents aged 18 and older was selected. The two-way table summarizes the relationship between marital status and housing status for these resident.

\(\begin{array}{l|c|c|c} & Married & Not married & Total \\ \hline Own & 172 & 82 & 254 \\ \hline Rent & 40 & 54 & 94 \\ \hline Total & 212 & 136 & 348 \end{array}\)

State the hypotheses for a test of the relationship between marital status and housing status for U.S. residents.

...