/*! 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 38 Of two personnel evaluation tech... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 38

Of two personnel evaluation techniques available, the first requires a 2-hour test-interview while the second can be completed in less than an hour. The scores for each of the eight individuals who took both tests are given in the next table. $$ \begin{array}{ccc} \text { Applicant } & \text { Test } 1(x) & \text { Test } 2(y) \\ \hline 1 & 75 & 38 \\ 2 & 89 & 56 \\ 3 & 60 & 35 \\ 4 & 71 & 45 \\ 5 & 92 & 59 \\ 6 & 105 & 70 \\ 7 & 55 & 31 \\ 8 & 87 & 52 \end{array} $$ a. Construct a scatterplot for the data. b. Describe the form, direction, and strength of the pattern in the scatterplot.

Short Answer

Expert verified
Answer: There is a strong positive relationship between scores on Test 1 and Test 2, suggesting that higher scores on one test are associated with higher scores on the other test.

Step by step solution

01

Determine x and y values for the scatterplot.

From the given table, the scores of Test 1 (x) and Test 2 (y) for all individuals will be used as x and y values in the scatterplot.
02

Plot the scatterplot

Using graph paper or a software, plot the scatterplot using the x and y values from the table. Put Test 1 on the x-axis and Test 2 on the y-axis. Plot each applicant's Test 1 score against their Test 2 score. The scatterplot should look like this with the points plotted: (75, 38), (89, 56), (60, 35), (71, 45), (92, 59), (105, 70), (55, 31), (87, 52)
03

Describe the form of the scatterplot

The form of a scatterplot is described by checking whether there is any specific shape or pattern to the plotted points. In this scatterplot, the points seem to follow a linear pattern, forming somewhat of a straight line.
04

Describe the direction of the scatterplot

The direction of a scatterplot shows how the two variables are related to each other. In this case, as Test 1 scores increase, the Test 2 scores also seem to increase. Therefore, the direction is positive since both variables increase together.
05

Describe the strength of the scatterplot

The strength of a scatterplot is determined by how closely the points follow the pattern or shape found in Step 3. Since the points in our scatterplot are quite close to the linear pattern, we can say that the strength is strong. In conclusion, the pattern in the scores of these two personnel evaluation tests is linear in form, positive in direction, and strong in strength. This suggests that there is a strong positive relationship between scores on Test 1 and Test 2, with higher scores on one test associated with higher scores on the other test.

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.

Linear Relationship
A linear relationship in a scatterplot indicates that as one variable increases, the other variable exhibits a predictable increase or decrease as well.
This predictable change is reflected as a straight line, or close to a straight line, when the data points are plotted. Understanding the concept of a linear relationship can be very helpful in various fields like economics, biology, and social sciences.

A key characteristic of a linear relationship is its simplicity, as it can be represented with a simple equation, typically of the form:
  • y = mx + b
Where:
  • y represents the dependent variable
  • x is the independent variable
  • m is the slope of the line, indicating the rate of change
  • b is the y-intercept, the value of y when x is zero
The data concerning the test scores in the original example demonstrates a linear relationship, as the points closely align to a straight path. Recognizing such patterns helps in predicting future outcomes based on your dataset.
Positive Correlation
In scatterplot analysis, a positive correlation is identified when two variables move in the same direction.
Simply put, when one variable increases, the other does too. This is an important concept in statistics and helps establish relationships between variables.
The scatterplot from the exercise shows a positive correlation between Test 1 and Test 2 scores. This positive relationship is clear because as Test 1 scores increase, Test 2 scores rise accordingly. Positive correlation is denoted mathematically as:
  • If correlation coefficient (r) > 0, it indicates a positive correlation
Understanding positive correlation is crucial for predicting outcomes and understanding the causal relationships between different factors. For instance, higher education levels tend to correlate positively with income levels.
Statistical Strength
Statistical strength assesses how closely data points in a scatterplot follow a discernible pattern or shape.
A strong statistical strength means that the data points are tightly packed around a line or curve, suggesting a reliable, predictable relationship. In contrast, weak statistical strength indicates more scattered data with less predictability.
Analyzing our personnel evaluation data, we determine the strength of the relationship by observing how close the plotted points are to forming a straight line. In this case, the points show a strong pattern which implies that scores from Test 1 and Test 2 are closely related.
Strength is often quantified using the correlation coefficient:
  • Strong positive correlation: close to +1
  • Strong negative correlation: close to -1
  • Weak correlation: close to 0
Understanding statistical strength allows us to make more informed decisions or predictions regarding the behavior of the variables involved. In practical applications, this can be used in fields like finance, healthcare, or technology to gauge the reliability of data trends.

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

Using a chemical procedure called differential pulse polarography, a chemist measured the peak current generated (in microamperes) when a solution containing a given amount of nickel (in parts per billion) is added to a buffer. The data are shown here: $$ \begin{array}{cc} x=\text { Ni (ppb) } & y=\text { Peak Current }(\mu \mathrm{A}) \\ \hline 19.1 & .095 \\ 38.2 & .174 \\ 57.3 & .256 \\ 76.2 & .348 \\ 95 & .429 \\ 114 & .500 \\ 131 & .580 \\ 150 & .651 \\ 170 & .722 \end{array} $$ Use a graph to describe the relationship between \(x\) and \(y .\) Add any numerical descriptive measures that are appropriate. Write a paragraph summarizing your results.

Suppose that the relationship between two variables \(x\) and \(y\) can be described by the regression line \(y=2.0+0.5 x.\) a. What is the change in \(y\) for a one-unit change in \(x\) ? b. Do the values of \(y\) increase or decrease as \(x\) increases? c. At what point does the line cross the \(y\) -axis? What is the name given to this value? d. If \(x=2.5,\) use the least squares equation to predict the value of \(y .\) What value would you predict if \(x=4.0 ?\)

Professor Isaac Asimov was one of the most prolific writers of all time. He wrote nearly 500 books during a 40 -year career prior to his death in \(1992 .\) In fact, as his career progressed, he became even more productive in terms of the number of books written within a given period of time. \(^{8}\) These data are the times (in months) required to write his books, in increments of 100: $$ \begin{array}{l|ccccc} \text { Number of Books } & 100 & 200 & 300 & 400 & 490 \\ \hline \text { Time (in months) } & 237 & 350 & 419 & 465 & 507 \end{array} $$ a. Plot the accumulated number of books as a function of time using a scatterplot. b. Describe the productivity of Professor Asimov in light of the data set graphed in part a. Does the relationship between the two variables seem to be linear?

The color distributions for two snacksize bags of \(\mathrm{M\&M}^{\prime} \mathrm{S}^{@}\) candies, one plain and one peanut, are displayed in the table. Choose an appropriate graphical method and compare the distributions. $$ \begin{array}{lrrrccc} & \text { Brown } & \text { Yellow } & \text { Red } & \text { Orange } & \text { Green } & \text { Blue } \\ \hline \text { Plain } & 15 & 14 & 12 & 4 & 5 & 6 \\ \text { Peanut } & 6 & 2 & 2 & 3 & 3 & 5 \end{array} $$

Male and female respondents to a questionnaire about gender differences are categorized into three groups according to their answers to the first question: $$ \begin{array}{lccc} & \text { Group 1 } & \text { Group 2 } & \text { Group 3 } \\ \hline \text { Men } & 37 & 49 & 72 \\ \text { Women } & 7 & 50 & 31 \end{array} $$ a. Create side-by-side pie charts to describe these data. b. Create a side-by-side bar chart to describe these data. c. Draw a stacked bar chart to describe these data. d. Which of the three charts best depicts the difference or similarity of the responses of men and women?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Pure 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.