/*! 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 90 Working mother In response to th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 90

Working mother In response to the statement on a recent General Social Survey, "A preschool child is likely to suffer if his or her mother works," suppose the response categories (strongly agree, agree, disagree, strongly disagree) had counts \((104,370,665,169) .\) Scores (2,1,-1,-2) were assigned to the four categories, to treat the variable as quantitative. Software reported a. Explain what this choice of scoring assumes about relative distances between categories of the scale. b. Based on this scoring, how would you interpret the sample mean of \(-0.1261 ?\) c. Explain how you could also make an inference about proportions for these data.

Short Answer

Expert verified
The scoring assumes equal distances between categories. A sample mean of -0.1261 indicates slight disagreement, suggesting most respondents somewhat disagreed with the statement.

Step by step solution

01

Understanding Scoring Assumptions

When scores (2, 1, -1, -2) are assigned to the categories (strongly agree, agree, disagree, strongly disagree), it assumes a uniform scale where the difference in intensity between neighboring categories is equal. This means moving from 'strongly agree' to 'agree' is considered a one-unit change, similar to moving from 'agree' to 'disagree' and from 'disagree' to 'strongly disagree.' Additionally, it treats the responses as numeric values on a symmetrical Likert scale, where negative values indicate disagreement and positive values indicate agreement.
02

Interpreting the Sample Mean

A sample mean of (-0.1261) indicates that on average, the respondents slightly disagree with the statement that a preschool child is likely to suffer if the mother works. Since the mean is closer to zero but on the negative side, there is a slight inclination towards disagreement, implying that more respondents overall leaned towards the categories 'disagree' and 'strongly disagree' than towards 'agreeing' categories.
03

Making Inferences about Proportions

To make inferences about proportions, one could examine the frequencies or proportions of each response category separately rather than treating the scale as continuous. This involves computing the proportion of responses in each category: 'strongly agree', 'agree', 'disagree', and 'strongly disagree'. By doing this, insights into how respondents tend to cluster around particular opinions can be drawn. For example, if a significant proportion falls into 'disagree' and 'strongly disagree', it suggests a majority disagreement with the statement.

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.

Likert scale interpretation
Likert scales are a popular tool used in surveys to measure attitudes or opinions. They usually consist of a series of statements with a range of response options, often categorically ordered from strong agreement to strong disagreement. In this case, we are interpreting a Likert scale with four categories: strongly agree, agree, disagree, and strongly disagree.
  • Symmetrical Scoring: The scale is symmetrical with positive scores assigned to agreement and negative scores to disagreement. This implies that agreement and disagreement are equally weighted on opposite sides of the neutral zero point.
  • Equal Distances: Scoring assumes equal intervals between each adjacent category. For example, the shift in attitude intensity from 'agree' to 'disagree' is viewed as similar to that from 'disagree' to 'strongly disagree'.
This kind of interpretation aids researchers in quantitatively analyzing subjective data, allowing complex attitudes to be distilled into comparable scores.
Quantitative scoring in surveys
Quantitative scoring takes qualitative survey responses and assigns them numerical values. This allows for mathematical analysis of data that was initially non-numerical.
  • Score Assignment: In the provided survey, scores of 2, 1, -1, and -2 are allocated to 'strongly agree', 'agree', 'disagree', and 'strongly disagree', respectively. Such scoring transforms subjective opinions into quantifiable data points, enabling more precise analysis.
  • Data Transformation: When you convert verbal responses to numbers, it opens up avenues for various statistical computations, like averages and variances, which help in drawing meaningful insights from the data.
This methodology provides a bridge between qualitative sentiments and quantitative analysis, essential for rigorous data examination in social research.
Sample mean analysis
The sample mean is a fundamental concept in statistical analysis, representing the average of all data points. It offers a quick snapshot of the general trend in your data.
  • Mean Calculation: Here, a sample mean of (-0.1261) has been computed from the scored responses. This mean is a weighted average of the scores corresponding to each response category, providing a single measure of central tendency.
  • Interpretation: A mean close to zero suggests a balanced view among respondents. However, the negative mean indicates a slight overall tendency towards disagreement, meaning more respondents leaned towards 'disagree' and 'strongly disagree' than towards agreement.
Through sample mean analysis, researchers can efficiently summarize large data sets and interpret the overarching sentiment or opinions of survey participants.
Proportional inference
Proportional inference in surveys refers to deducing insights based on the relative frequency of each response category. This technique offers a granular understanding of opinion distribution.
  • Category Proportions: By calculating the proportion of responses in each category, researchers can see how opinions divide among the options. This involves tallying responses and converting these counts into percentages of the total responses.
  • Insight Extraction: For instance, if a substantial percentage of participants choose 'disagree' and 'strongly disagree', this implies a broader disagreement among the cohort. On the other hand, an equal distribution across categories may indicate mixed or balanced opinions.
Proportional inference helps identify dominant trends and clusters in attitudes, which is invaluable when nuanced understanding of public opinion is needed.
Survey response analysis
Survey response analysis encompasses various techniques to scrutinize collected data, ensuring meaningful interpretations.
  • Data Cleaning: Initially, survey data is often refined to exclude incomplete or invalid responses, ensuring that the analysis reflects valid opinions.
  • Statistical Techniques: Analysts leverage tools like means, proportions, correlations, and regressions to dissect the survey data. Each technique provides a different lens through which to view the data, enabling comprehensive understanding.
  • Practical Application: Using software for analysis allows for streamlined and accurate processing. For instance, seeing a software-generated sample mean can quickly communicate overall trends in the dataset.
Effective survey response analysis transforms raw data into actionable insights, supporting informed decision-making processes in research and business environments.

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

True or false If you have a volunteer sample instead of a random sample, then a confidence interval for a parameter is still completely reliable as long as the sample size is larger than about 30 .

Women's satisfaction with appearance A special issue of Newsweek in March 1999 on women and their health reported results of a poll of 757 American women aged 18 or older. When asked, "How satisfied are you with your overall physical appearance?" \(30 \%\) said very satisfied, \(54 \%\) said somewhat satisfied, \(13 \%\) said not too satisfied, and \(3 \%\) said not at all satisfied. True or false: Since all these percentages are based on the same sample size, they all have the same margin of error.

What affects n? Using the sample size formula \(n=\left[\hat{p}(1-\hat{p}) z^{2}\right] / m^{2}\) for a proportion, explain the effect on \(n\) of (a) increasing the confidence level and (b) decreasing the margin of error.

Exit poll predictions A national television network takes an exit poll of 1400 voters after each has cast a vote in a state gubernatorial election. Of them, 660 say they voted for the Democratic candidate and 740 say they voted for the Republican candidate. a. Treating the sample as a random sample from the population of all voters, would you predict the winner? Base your decision on a \(95 \%\) confidence interval. b. Base your decision on a \(99 \%\) confidence interval. Explain why you need stronger evidence to make a prediction when you want greater confidence.

Fear of breast cancer A recent survey of 1000 American women between the ages of 45 and 64 asked them what medical condition they most feared. Of those sampled, \(61 \%\) said breast cancer, \(8 \%\) said heart disease, and the rest picked other conditions. By contrast, currently about \(3 \%\) of female deaths are due to breast cancer, whereas \(32 \%\) are due to heart disease. \(^{5}\) a. Construct a \(90 \%\) confidence interval for the population proportion of women who most feared breast cancer. Interpret. b. Indicate the assumptions you must make for the inference in part a to be valid.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision 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.