/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 43 Female for president? When recen... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 43

Female for president? When recent General Social Surveys have asked, "If your party nominated a woman for president, would you vote for her if she were qualified for the job?" about \(94 \%\) of females and \(94 \%\) of males answered yes, the rest answered no. (Source: Data from CSM, UC Berkeley.) a. For males and for females, report the conditional distributions on this response variable in a \(2 \times 2\) table, using outcome categories (yes, no). b. If results for the entire population are similar to these, does it seem possible that gender and opinion about having a woman president are independent? Explain.

Short Answer

Expert verified
The conditional distributions show no difference; gender and opinion appear independent.

Step by step solution

01

Understand the problem

The problem provides survey data that suggests that 94% of both females and males would vote yes for a qualified female president. We need to summarize this data in a table and discuss the independence of gender and opinion.
02

Construct conditional distribution table

For both males and females, we need to create a table with categories (yes, no). Let's assign these percentages in a 2x2 table. | Gender | Yes | No | | ------- | ----- | ---- | | Female | 94% | 6% | | Male | 94% | 6% | This table shows the conditional distribution for both genders concerning their willingness to vote for a female president.
03

Assess Independence

To determine if gender and opinion are independent, we look for any differences in responses between genders. If gender and opinion are independent, the percentage responses (yes or no) should be similar across genders. Since the percentage of both males and females who respond yes is the same (94%), there is no evidence of a dependency between gender and opinion about voting for a female president.
04

Conclusion

Given the uniform distribution of responses, it seems that gender and opinion about having a female president are statistically independent. This is because an equal proportion of both males and females responded positively, which suggests no interaction effect of gender on the choice.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Independence Test
An independence test in statistics helps us determine whether two categorical variables are related. In this context, we examine whether gender (male or female) and opinion about voting for a female president are independent of each other.
The process involves comparing observed data with expected data if the variables were indeed independent. For our exercise, we have identical percentages: 94% say "yes" across both genders.
If both males and females show the same willingness to vote "yes," this can be taken as evidence supporting the hypothesis that these two factors鈥攇ender and voting opinion鈥攁re possibly unrelated, or independent. An independence test provides an objective way to support such conclusions with statistical evidence.
Survey Data Analysis
Survey data analysis is pivotal for extracting meaningful information from responses collected. Here, we are working with the responses from a general survey where people were asked if they'd vote for a woman president.
This type of analysis helps us:
  • Understand the proportions of responses (e.g., the 94% 'yes' rate)
  • Create visual summaries such as tables for clarity
  • See trends or differences among subgroups, like male versus female
For this exercise, the survey data suggests no significant variation in opinion between genders regarding voting for a woman president. The uniformity in responses (with 94% from both groups) simplifies our analysis and strengthens our conclusion drawn from such data.
Statistical Independence
Statistical independence refers to two variables not affecting each other鈥檚 outcomes. In simpler terms, knowing the outcome of one doesn't change the probability of the other. In our survey, both genders gave the same percentage of positive responses. This convergence implies that gender doesn't significantly impact opinions on supporting a female presidential candidate.
To verify statistical independence, ideally, one would use tests like the Chi-square test. Although not in the original step-by-step solution, it reinforces the points. When applied, such a test further supports the absence of dependency between gender and opinion, aligning with the empirical data we've seen. Thus, statistical independence here means gender and voting opinion statistically do not influence each other in this context.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Pregnancy associated with contraceptive use? Whether or not a young married woman becomes pregnant in the next year is a categorical variable with categories (yes, no). Another categorical variable to consider is whether she and her partner use contraceptives with categories (yes, no). Would you expect these variables to be independent, or associated? Explain.

Normal and chi-squared with \(d f=1\) When \(d f=1\), the P-value from the chi- squared test of independence is the same as the P-value for the two-sided test comparing two proportions with the \(z\) test statistic. This is because of a direct connection between the standard normal distribution and the chi-squared distribution with \(d f=1\) : Squaring a \(z\) -score yields a chi-squared value with \(d f=1\) having chi- squared right-tail probability equal to the twotail normal probability for the \(z\) -score. a. Illustrate this with \(z=1.96,\) the \(z\) -score with a twotail probability of \(0.05 .\) Using the chi-squared table or software, show that the square of 1.96 is the chisquared score for \(d f=1\) with a P-value of 0.05 . b. Show the connection between the normal and chisquared values with \(\mathrm{P}\) -value \(=0.01\)

Variability of chi-squared For the chi-squared distribution, the mean equals \(d f\) and the standard deviation equals \(\sqrt{2(d f)}\) a. Explain why, as a rough approximation, for a large \(d f\) value, \(95 \%\) of the chi-squared distribution falls within \(d f \pm 2 \sqrt{2(d f)}\) b. With \(d f=8,\) show that \(d f \pm 2 \sqrt{2(d f)}\) gives the interval (0,16) for approximately containing \(95 \%\) of the distribution. Using the chi- squared table, show that exactly \(95 \%\) of the distribution actually falls between 0 and \(15.5 .\)

Down syndrome diagnostic test The table shown, from Example 8 in Chapter \(5,\) cross-tabulates whether a fetus has Down syndrome by whether or not the triple blood diagnostic test for Down syndrome is positive (that is, indicates that the fetus has Down syndrome). a. Tabulate the conditional distributions for the blood test result, given the true Down syndrome status. b. For the Down cases, what percentage was diagnosed as positive by the diagnostic test? For the unaffected cases, what percentage got a negative test result? Does the diagnostic test appear to be a good one? c. Construct the conditional distribution on Down syndrome status, for those who have a positive test result. (Hint: You condition on the first column total and find proportions in that column.) Of those cases, what percentage truly have Down syndrome? Is the result surprising? Explain why this probability is small.

What is independent of happiness? Which one of the following variables would you think most likely to be independent of happiness: belief in an afterlife, family income, quality of health, region of the country in which you live, satisfaction with job? Explain the basis of your reasoning.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.