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SECONDARY
STATISTICS AND PROBABILITY
HIGH SCHOOL STATISTICS
TWO-WAY TABLES
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Calculus and Analysis
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Two-way tables Answers
Two-way tables
asked 2021-03-08
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 residents.
\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{c}\right|}{c}{\mid}{c}\right\rbrace}&{M}{a}{r}{r}{i}{e}{d}&{N}{o}{t}{m}{a}{r}{r}{i}{e}{d}&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{O}{w}{n}&{172}&{82}&{254}\backslash{h}{l}\in{e}{R}{e}{n}{t}&{40}&{54}&{94}\backslash{h}{l}\in{e}{T}{o}{t}{a}{l}&{212}&{136}&{348}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
Two-way tables
asked 2021-03-05
1950 randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the two-way classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off, the same as, or worse off than their parents
\(\begin{array}{|c|c|c|}\hline &\text{Less Than High School}&\text{High School}&\text{More Than High School}\\\hline \text{Better off} &140&440&430\\ \hline \text{Same as}&60&230&110\\ \hline \text{Worse off}&180&280&80\\ \hline\end{array}\\\)
Suppose one adult is selected at random from these 1950 adults. Find the following probablity.
Round your answer to three decimal places.
\(P(\text{more than high school or worse off})=?\)
Two-way tables
asked 2021-03-04
How are the smoking habits of students related to their parents' smoking? Here is a two-way table from a survey of student s in eight Arizona high schools:
\(\begin{array}{c|c}&\text{Student smokes}&\text{Student does not smoke}&\text{Total}\\\hline\text{Both parents smoke}&400&1380&400+1380=1780\\\hline\text{One parent smokes}&416&1823&416+1823=2239\\\hline\text{Neither parent smokes}&188&1168&188+1168=1356\\\hline\text{Total}&400+416+188=1004&1380+1823+1168=4371&1004+4371=5375\end{array}\)
(a) Write the null and alternative hypotheses for the question of interest.
(b) Find the expected cell counts. Write a sentence that explains in simple language what "expected counts" are.
(c) Find the chi-square statistic, its degrees of freedom, and the P-value.
(d) What is your conclusion about significance?
Two-way tables
asked 2021-03-02
When performing a
\(\displaystyleχ^{{2}}\)
test of independent in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statistic in each of the following circumstances:
a. α=0.05, r=4 rows, c=5 columns
b. α=0.01, r=4 rows, c=5 columns
c. α=0.01, r=4 rows, c=6 columns
d. α=0.01, r=3 rows, c=6 columns
e. α=0.01, r=6 rows, c=3 columns
Two-way tables
asked 2021-03-02
In a General Social Survey of Americans in 1991, two variables, gender and finding life exciting or dull, were measured on 980 individuals. The two-way table below summarizes the results.
Let A = randomly chosen person is female
Let B = randomly chosen person finds life exciting
(a) Find P(A | B)
(b) Are the events A & B independent?
\(\begin{array}{ccc}\text{Original Counts}&\text{Exciting}&\text{Routine}&\text{Dull}&\text{Total}\\\hline \text{Male} &213&200&12&425\\ \text{Female}&221&305&29&555\\ \text{Female}&434&505&41&980 \end{array}\)
Two-way tables
asked 2021-02-23
Give the degrees of freedom for the chi-square test based on the two-way table.
\(\begin{array}{|c|c|c|} \hline &\text{Yes}&\text{No}&\text{Total}\\ \hline \text{Group 1} & 56&44&100\\ \hline \text{Group 2}&132&68&200\\ \hline \text{Group 3}&72&28&100\\ \hline \text{Total}&260&140&400\\ \hline \end{array}\)
Degrees of freedom=?
Two-way tables
asked 2021-02-13
Men and women were surveyed regarding their favorite leisure sport, as shown below. All questions pertain to this two-way frequency table.
\(\begin{array}{|c|c|c|}\hline\text{Leisure Sport}&\text{Golf}&\text{Tennis}&\text{Skiing}&\text{Total}\\\hline\text{Men} &32 & 21 & 30&83\\ \hline\text{Women}& 35 & 30&26&91\\\hline \ \text{Total}&67&51&56&174 \\ \hline \end{array}\)
\(\text{Find P(men)} \cdot \text{P(skiing)}.\)
(Choose a numbered choice from the list below.)
\(1) \frac{83}{174}\)
\(2) \frac{56}{174}4\)
\(3) \frac{4648}{174}\)
\(4) \frac{4648}{174^2}\)
Two-way tables
asked 2021-02-12
In 1912 the Titanic struck an iceberg and sank on its first voyage. Some passengers got off the ship in lifeboats, but many died. The following two-way table gives information about adult passengers who survived and who died, by class of travel.
\(\begin{array} {lc} & \text{Class} \ \text {Survived } & \begin{array}{c|c|c|c} & \text { First } & \text { Second } & \text { Third } \\ \hline \text { Yes } & 197 & 94 & 151 \\ \hline \text { No } & 122 & 167 & 476 \end{array}\ \end{array}\)
Suppose we randomly select one of the adult passengers who rode on the Titanic. Define event D as getting a person who died and event F as getting a passenger in first class. Find P(not a passenger in first class or survived).
Two-way tables
asked 2021-02-08
This two-way table shows the results of asking students if they prefer to have gym class in the morning or the afternoon A.How many students participate in the survey B. How many students in grade 8 prefer to have gym in the morning C. How many grade 10 students participated in the survey D. How many students prefer To have gym in the afternoon
\(\begin{array}{|c|c|c|}\hline&\text{morning}&\text{afternoon}&\text{total}\\\hline\text{grade 6} &15 & 8 & 23\\ \hline\text{grade 8}& 18 & 21&39\\\hline\text{grade 10}& 12 & 26&38\\ \hline \text{total}&45&55&100 \\ \hline \end{array}\)
Two-way tables
asked 2021-01-31
Use the two-way table below to answer the following question. Round the answer to the nearest whole percent. There are 300 seniors at Bellmere Senior High School who are enrolled in elective science classes as shown below.
\(\begin{array}{c|cc|c} &\text{Physics}&\text{Chemistry}&\text{Total}\\ \hline \text{Males}&100&68&168\\ \text{Females}&71&61&132\\ \hline \text{Total}&171&129&300 \end{array}\\)
What is the probability that a senior student chosen at random is enrolled in physics given that student is female?
Two-way tables
asked 2021-01-30
Gastric freezing was once a recommended treatment for ulcers in the upper intestine. One experiment compared 82 subjects randomly assigned to gastric freezing and 78 subjects randomly assigned to receive a placebo. The two-way table shows the results of the experiment. Is there convincing evidence of an association between treatment and outcome for subjects like these?
\(\begin{array}{c|cc|c} & \text { Gastric freezing } &\text{Placebo}& \text { Total } \\ \hline \text { Improved } & 28 & 30 & 58 \\\text { Didn't improve} & 54 & 48 & 102 \\ \hline \text { Total } & 82 & 78 & 160\\ \end{array}\\)
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.
Two-way tables
asked 2021-01-27
One hundred adults and children were randomly selected and asked whether they spoke more than one language fluently. The data were recorded in a two-way table. Maria and Brennan each used the data to make the tables of joint relative frequencies shown below, but their results are slightly different. The difference is shaded. Can you tell by looking at the tables which of them made an error? Explain.
\(\begin{array}{c|c}&Yes&No\\\hline\text{Children}&0.15&0.25\\\hline\text{Adults}&0.1&0.6\end{array}\)
Two-way tables
asked 2021-01-19
The following is a two-way table showing preferences for an award (A, B, C) by gender for the students sampled in survey. Test whether the data indicate there is some association between gender and preferred award.
\(\begin{array}{|c|c|c|}\hline &\text{A}&\text{B}&\text{C}&\text{Total}\\\hline \text{Female} &20&76&73&169\\ \hline \text{Male}&11&73&109&193 \\ \hline \text{Total}&31&149&182&360 \\ \hline \end{array}\\\)
Chi-square statistic=?
p-value=?
Conclusion: (reject or do not reject
\(H_0\)
)
Does the test indicate an association between gender and preferred award? (yes/no)
Two-way tables
asked 2021-01-19
How is a two-way table used when determining possible associations between two different categories from the same sample group?
Two-way tables
asked 2021-01-16
Find the expected count and the contribution to the chi-square statistic for the (Group 1, No) cell in the two-way table below.
\(\begin{array}{|c|c|c|}\hline&\text{Yes}&\text{No}&\text{Total}\\\hline\text{Group 1} &56 & 42 & 98\\ \hline \ \text{Group 2}&135&67&202 \\ \hline \text{Group 3}&66&23&89 \\ \hline \text{Total}&257&132&389 \\ \hline \end{array}\)
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 = ?
Two-way tables
asked 2021-01-15
Two children own two-way radios that have a maximum range of 2 miles. One leaves a certain point at 1:00 P.M., walking due north at a rate of 4 . The other leaves the same point at 1:15 P.M., traveling due south at 6 . When will they be unable to communicate with one another?
Two-way tables
asked 2021-01-13
Below is a two-way frequency table. Which of the following frequencies show the proportion of male respondents who are in the chess club?
\(\begin{array}{|c|c|c|c|}\hline&\text{Intramural Basketball}&\text{Chess Club}&\text{Jazz Band}&\text{Not Involved}&\text{Total}\\\hline\text{Females} &20 & 10&10&20&60 \\ \hline\text{Males}& 20 & 2&8&10&40\\\hline\text{Total}&40&12&18&30&100\\\hline \end{array}\)
\(a)\frac{2}{10}=0.20\)
\(b)\frac{2}{40}=0.05\)
\(c)\frac{2}{12}\approx0.167\)
\(d)\frac{2}{100}=0.02\)
Two-way tables
asked 2021-01-08
Create and conduct a survey in your class. Organize the results in a two-way table. Then create a two-way table that shows the joint and marginal frequencies.
Two-way tables
asked 2021-01-06
The following table gives a two-way classification of all basketball players at a state university who began their college careers between 2004 and 2008, based on gender and whether or not they graduated.
\(\begin{array}{|c|c|c|}\hline &\text{Graduated}&\text{Did not Graduate}\\\hline \text{Male} &129&51\\ \hline \text{Female}&134&36 \\ \hline \end{array}\\\)
If one of these players is selected at random, find the following probability.
Round your answer to four decimal places.
\(P(\text{graduated or male})=\)
Enter your answer in accordance to the question statement
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