/*! 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 41 Suppose a college career center ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 41

Suppose a college career center was interested in the starting salaries of recent graduates in Communications Studies and Sociology. The center randomly samples 15 recent graduates from each of these fields and records the starting salary for the graduates. The center wants to determine whether there is a difference in the starting salaries for graduates in these majors. Which test(s) should be used in each of these situations? a. Assume the starting salary for both majors is approximately Normally distributed. b. Assume that one of the salary distributions is strongly right-skewed.

Short Answer

Expert verified
a. Independent two-sample t-test. b. Mann-Whitney U test.

Step by step solution

01

Situation A: Normally Distributed Salaries

When the starting salaries for both majors are approximately Normally distributed, the appropriate test to use is the independent two-sample t-test. The t-test is robust to the assumption of normality and compares the means of two groups. To perform the t-test, list the starting salary data for both majors, calculate the mean and variance for each group, then use these values in the t-test formula.
02

Situation B: One Salary Distribution is Strongly Right-Skewed

If one of the salary distributions is strongly right-skewed, i.e., it has a tail on the right side, indicating a few very high values, then the distribution deviates from normality. In this case, the appropriate test to use is the non-parametric Mann-Whitney U test (also known as the Wilcoxon rank-sum test). This test does not require the assumption of normal distribution and can handle skewed data. To perform this test, you will rank all the data from both groups together, then add up the ranks for each group and use these sums in the Mann-Whitney U test formula.

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!

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

Suppose you want to determine whether there is difference in wait times at two Department of Motor Vehicles offices. A random sample of customer wait times is obtained for each office. Which test(s) can be used for each situation below? a. The populaton distribution of wait times is approximately Normal for both groups b. The population distribution of wait times for one of the offices is skewed left.

You have recorded the time slept on a Tuesday and the time slept on a Sunday for a random sample of 15 students. You want to investigate whether students tend to sleep more on weekends than on weekdays. Which test(s) can you use? Answer for each circumstance. a. Assume the distribution of sleep hours for both Tuesday and Sunday are approximately Normal. b. Assume the distribution of sleep hours for both Tuesday and Sunday are not approximately Normal and assume that the distribution of differences in sleep hours for each student is not Normal. c. Assume the distributions of sleep hours for both Tuesday and Sunday are not Normal but assume the distribution of the differences in sleep hours is approximately Normal.

The California Department of Education assesses progress of \(\mathrm{K}-12\) students in meeting grade level standards in English/Language Arts and Mathematics yearly. A regression analysis was performed using 2016 assessment data from a sample of 195 California schools. The data consisted of the percentage of students at each school who met or exceeded the grade-level standards in English/Language Arts (SELA) and Mathematics (SMATH). Assume all conditions for the linear regression model hold. a. Using the information in the regression analysis output, is there a linear association between these two variables? Explain. b. Interpret the slope of the regression equation. c. Using a \(95 \%\) confidence interval, what is the estimated mean percent of mathematics proficient students at schools in which \(50 \%\) of students are proficient in English/Language Arts?

a. Find the log (base 10) of each number. Round off to one decimal place as needed. 10, 10000, 1500, 5 b. The following numbers are in log units. Do the back transformation by finding the antilog (base 10) of these numbers. Round off to one decimal place as needed. 2, 3, 1.5, 2.4

The registrar at a small college says she can predict the number of units that a full-time student has accumulated on the basis of the number of semesters the student has attended the college by using the equation Predicted Units \(=0+14\) Semesters This tells us the deterministic part of the regression model. What factors might contribute to the random component? In other words, why might a student's number of units not fall exactly on this line?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.