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&Nohlinetext{Children}&0.15&0.25hlinetext{Adults}&0.1&0.6end{array}

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&Nohlinetext{Children}&0.15&0.25hlinetext{Adults}&0.1&0.6end{array}

Question
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.
\(\begin{array}{c|c}&Yes&No\\\hline\text{Children}&0.15&0.25\\\hline\text{Adults}&0.1&0.6\end{array}\)

Answers (1)

2021-01-28
We determine the marginal relative frequencies using Maria's table:
\(\begin{array}{c|c}&Yes&No&\text{Total}\\\hline\text{Children}&0.15&0.25&0.40\\\hline\text{Adults}&0.1&0.6&0.7\\\hline\text{Total}&0.25&0.85&1.1\end{array}\)
We determine the marginal relative frequencies using Brennan's table:
\(\begin{array}{c|c}&Yes&No&\text{Total}\\\hline\text{Children}&0.15&0.25&0.40\\\hline\text{Adults}&0.1&0.5&0.6\\\hline\text{Total}&0.25&0.75&1.0\end{array}\)
Maris's table is wrong because the number in the lower right cell is not 1. Brennan's table is correct.
Result: Maria's table
0

Relevant Questions

asked 2021-03-05
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asked 2021-02-25
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asked 2020-10-23
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
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b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P \((A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).\)
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
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f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
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i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
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asked 2021-01-25

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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 2020-12-29

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asked 2021-01-10
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\((b) \frac{20}{125}\)
\((c) \frac{80}{125}\)
\((d) \frac{90}{125}\)
\((e) \frac{110}{125}\)
asked 2021-01-27
Researchers carried out a survey of fourth-, fifth- and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.
\(\begin{array}{c|c}& 4th\ grade & 5th\ grade & 6th\ grade &Total \\ \hline Grades &49&50&69&168\\ \text{Athletic} &24&36&38&98\\ \text{Popular}\ &19&22&28&69\\ \hline \text{Total} & 92 & 108 & 135 &335 \end{array}\)
Suppose we select one of these students at random. What's the probability of each of the following? The student is a sixth-grader or rated good grades as Important.
asked 2021-02-09
Researchers carried out a survey of fourth-, fifth- and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.
\(\begin{array}{c|c} & 4th\ grade & 5th\ grade & 6th\ grade &Total \\ \hline Grades &49&50&69&168\\ Athletic &24&36&38&98\\ Popular\ &19&22&28&69\\ \hline Total & 92 & 108 & 135 &335 \end{array}\)
Suppose we select one of these students at random. What's the probability of each of the following? The student is not a sixth-grader and did not rate good grades as important.
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