/*! 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 89 Are Female Rats More Compassiona... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 89

Are Female Rats More Compassionate Than Male Rats? Exercise 3.88 describes a study in which rats showed compassion by freeing a trapped rat. In the study, all six of the six female rats showed compassion by freeing the trapped rat while 17 of the 24 male rats did so. Use the results of this study to give a best estimate for the difference in proportion of rats showing compassion, between female rats and male rats. Then use StatKey or other technology to estimate the standard error \(^{44}\) and use it to compute a \(95 \%\) confidence interval for the difference in proportions. Use the interval to determine whether it is plausible that male and female rats are equally compassionate (i.e., that the difference in proportions is zero). The data are available in the dataset CompassionateRats.

Short Answer

Expert verified
The statistical analysis for the exercise isn't fully feasible due to the lack of a standard error value in the exercise, however, the preliminary steps have been outlined. The proportions of compassionate behavior were calculated for both genders, with a difference observed. Further statistical methods would need to be employed to conclusively say if the observed difference is significant.

Step by step solution

01

Determine the Proportions

For the female rats, the proportion showing compassion is calculated as the number of compassionate females divided by the total number of females. Here, all six female rats showed compassion, so the proportion is \(6/6 = 1\).For the male rats, the proportion showing compassion is calculated as the number of compassionate males divided by the total number of males. In this case, 17 out of 24 male rats showed compassion, so the proportion is \(17/24 \approx 0.7083\).
02

Compute the Difference in Proportions

Now subtract the proportion of compassionate males from the proportion of compassionate females to get the difference in proportions: \(1 - 0.7083 \approx 0.2917\). This is the best estimate for the difference in the proportion of rats showing compassion between female and male rats.
03

Estimate the Standard Error

Next, use statistical methods (such as StatKey or similar software) to calculate the standard error of the difference. Given no specific data or formula structure provided in question to calculate standard error directly, we accept it as a step, but won't be able to provide a precise numerical result.
04

Compute the Confidence Interval

After getting the standard error, construct a 95% confidence interval for the difference in proportions. Multiply the standard error (SE) by 1.96 (the z-score for a 95% confidence interval) and add and subtract this amount from the difference in proportions to give the lower and upper bounds of the confidence interval. The interval should look like this: \(0.2917 \pm 1.96*SE\).
05

Evaluate the Hypothesis

Finally, examine the confidence interval to determine whether it is plausible for the difference in proportions to be zero. If the interval contains zero, it indicates that the true difference in proportions could be zero, hence, it would be plausible that male and female rats are equally compassionate. But if the confidence interval does not contain zero, that indicates the true difference is not likely to be zero and it would not be plausible that male and female rats are equally compassionate. Again, due to lack of standard error numerical value in exercise, this step can't be executed with a definitive answer.

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.

Difference in Proportions
In statistics, the difference in proportions is a powerful tool to compare two groups. It allows us to understand and analyze how one group differs from another in terms of a particular characteristic or behavior. Here, we look at how the proportion of compassionate behavior differs between female and male rats.
  • For female rats, the compassion rate was 100% since all 6 showed the behavior. Hence, their proportion is \( \frac{6}{6} = 1 \).
  • For male rats, 17 out of 24 showed compassion, making their proportion about \( \frac{17}{24} \approx 0.7083 \).
  • The difference in proportions is calculated by subtracting the male proportion from the female proportion: \( 1 - 0.7083 \approx 0.2917 \).
This difference, \( 0.2917 \), is our best estimate of how much more likely female rats are to exhibit compassion compared to male rats. In statistical studies like this, such differences help identify significant behavioral trends between different groups.
Statistical Hypothesis Testing
Statistical hypothesis testing is a method to determine if there is enough evidence to reject a null hypothesis. In this study with rats, we want to see if it's plausible that male and female rats are equally compassionate, meaning the difference in proportions would be zero.
To test this, we rely on a calculated confidence interval.
  • The null hypothesis (\( H_0 \)): There is no difference in compassion between male and female rats. Thus, the difference in proportions is zero.
  • The alternative hypothesis (\( H_a \)): There is a difference in compassion, implying the proportions are not equal.
  • We calculate a 95% confidence interval for the difference in proportions. If this interval contains zero, the null hypothesis could be true.
A confidence interval offers a range of values representing where the true difference might lie. If zero is included in this range, we cannot say there's a significant difference. Conversely, if zero falls outside the interval, it implies a likely difference in compassion levels between the two groups.
Rat Compassion Study
The Rat Compassion Study investigates whether female rats display more compassion than their male counterparts by attempting to free a trapped rat. Compassion in animals can reflect complex behavioral traits and help in understanding social behaviors.
h4: Study Setup In this study:
  • All 6 female rats freed the caged rat, indicating a perfect proportion of compassion.
  • Out of 24 male rats, 17 showed the same behavior.
  • The study aims to use this data to quantify and compare compassion levels statistically.
Understanding compassion in rats can offer insights into social behaviors that are applicable in broader animal behavior studies. These findings can influence ideas about gender differences in empathy and cooperation, making them essential in animal behavior research.
Tools like confidence intervals and hypothesis testing bridge empirical observations with statistical verification, allowing for a structured analysis of behavioral data. This approach not only provides a better understanding of compassion in rats but can also have implications for how compassion is studied across different species and genders.

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

College Graduates In Example 3.1 on page 197, we see that \(27.5 \%\) of US adults are college graduates. (a) Use StatKey or other technology to generate a sampling distribution for the sample proportion of college graduates using a sample size of \(n=50 .\) Generate at least 1000 sample proportions. Give the shape and center of the sampling distribution and give the standard error. (b) Repeat part (a) using a sample size of \(n=500\).

What Proportion Believe in One True Love? In Data 2.1 on page 48 , we describe a study in which a random sample of 2625 US adults were asked whether they agree or disagree that there is "only one true love for each person." The study tells us that 735 of those polled said they agree with the statement. The standard error for this sample proportion is \(0.009 .\) Define the parameter being estimated, give the best estimate, the margin of error, and find and interpret a \(95 \%\) confidence interval.

Investigating the Width of a Confidence Interval Comparing Exercise 3.120 to Exercise \(3.121,\) you should have found that the confidence interval when utilizing the paired structure of the data was narrower than the confidence interval ignoring this structure (this will generally be the case, and is the primary reason for pairing). How else could we change the width of the confidence interval? More specifically, for each of the following changes, would the width of the confidence interval likely increase, decrease, or remain the same? (a) Increase the sample size. (b) Simulate more bootstrap samples. (c) Decrease the confidence level from \(99 \%\) to \(95 \%\).

How Important Is Regular Exercise? In a recent poll \(^{50}\) of 1000 American adults, the number saying that exercise is an important part of daily life was 753 , Use StatKey or other technology to find and interpret a \(90 \%\) confidence interval for the proportion of American adults who think exercise is an important part of daily life.

3.62 Employer-Based Health Insurance A report from a Gallup poll \(^{29}\) in 2011 started by saying, "Forty-five percent of American adults reported getting their health insurance from an employer...." Later in the article we find information on the sampling method, "a random sample of 147,291 adults, aged 18 and over, living in the US," and a sentence about the accuracy of the results, "the maximum margin of sampling error is 卤1 percentage point." (a) What is the population? What is the sample? What is the population parameter of interest? What is the relevant statistic? (b) Use the margin of error \(^{30}\) to give an interval showing plausible values for the parameter of interest. Interpret it in terms of getting health insurance from an employer.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

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.