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Look again at the table summarizing the Roper survey in Exercise 15. a) If we select a respondent at random, what’s the probability we choose a person from the United States who has done post-graduate study? b) Among the respondents who have done post-graduate study, what’s the probability the person is from the United States? c) What’s the probability that a respondent from the United States has done post graduate study? d) What’s the probability that a respondent from China has only a primary-level education? e) What’s the probability that a respondent with only a primary-level education is from China?

   Look again at the table summarizing the Roper survey in Exercise 15.
a) If we select a respondent at random, what’s the probability we choose a person from the United States who has done post-graduate study?
b) Among the respondents who have done post-graduate study, what’s the probability the person is from the United States?
c) What’s the probability that a respondent from the United States has done post graduate study?
d) What’s the probability that a respondent from China has only a primary-level education?
e) What’s the probability that a respondent with only a primary-level education is from China?

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STATS Modeling The World

STATS Modeling The World

David E. Bock, Paul… 4th Edition

Chapter 4, Problem 21

Instant Answer

Solved by Expert Cathy Wang

05/29/2020

Step 1

The table presents different countries (China, France, India, UK, US) and different levels of education (postgraduate, college, high school, primary or less, no answer). The total number of respondents in the survey is 7690. Show more…

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Key Concepts

Contingency Table Analysis

Contingency table analysis involves organizing data into a matrix where rows and columns represent different categorical variables. This structure allows for the systematic computation of probabilities, joint probabilities, and conditional probabilities by using the counts in each cell relative to the total sample size.

Random Sampling

Random sampling is a fundamental concept in probability that ensures each member of a population has an equal chance of being selected. This principle underpins the validity of the probability calculations derived from survey data, ensuring that the computed probabilities accurately represent the population.

Joint Probability

Joint probability refers to the likelihood of two events occurring at the same time. In a survey or data table, it represents the probability that a respondent meets two criteria simultaneously, such as being from a specific country and having attained a certain level of education.

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred. It is calculated by dividing the joint probability of the two events by the probability of the condition, and it is key in understanding relationships and dependencies between different survey categories.

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Transcript

00:02 So for these questions, we need to use a table in the exercise 15.

00:08 So let's go back to the exercise 15 to see the table.

00:12 For this table, we have six rows and six columns.

00:18 For each shows, it represents a different country.

00:21 They are china, france, india, uk and u .s.

00:25 And for the column, it represents different education level, postgraduate colleagues, high school, primary, class, no answer.

00:34 And it also has one total column, one total rose.

00:40 And we know that the total number of the table is 7 -690.

00:48 And then let's go back to the questions.

00:51 The question is the probability that a person from a united states who has done a post -gradary study, here i write as a probability that a person from united states and the postgraduate study, i write g.

01:13 Yeah, what we need to do is go back to the table and find the us roles and the postgraduate columns and find intersection.

01:24 The number is 84.

01:27 So the probability here is equals to 84 divided by the total number 7 ,669.

01:34 It approximately equals to 0 .01.

01:42 Yeah, and problem b is probability that a person from united states who have done for postgraduate study.

01:55 So here is different from problem a, since it's a conditional probability.

02:01 And it's a probability that the person from united states, given that he has already done postgraduate study.

02:14 Here we should use a conditional formula to calculate this equals to p us and postgraduate study divided by the postgraduate study probability.

02:28 And go back to the table, we can find the probability us and the postgraduate study is 84 divided by 7690.

02:45 And the probability that post -graduate study is a total number in the first column, yes, 3 -79 over 7 -690.

03:02 It equals to 84 over 379, approximately equals to 0 .22.

03:17 Question c, is...