Chapter 9, Problem 20P

BuyFind*arrow_forward*

8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

An example of the vertical-horizontal illusion is shown in the figure. Although the two lines are exactly the same length, the vertical line appears to be much longer. To examine the strength of this illusion, a researcher prepared an example in which both lines were exactly 10 inches long. The example was shown to individual participants who were told that the horizontal line was 10 inches long and then were asked to estimate the length of the vertical line. For a sample of *n* = 25 participants, the average estimate was *M =* 12.2 inches with a standard deviation of *s* = 1.00.

**a.** Use a one-tailed hypothesis test with α = .01 to demonstrate that the individuals in the sample significantly overestimate the true length of the line. *(Note:* Accurate estimation would produce a mean of μ - 10 inches.)

**b.** Calculate the estimated *d* and *r*^{2}, the percentage of variance accounted for, to measure the size of this effect.

**c.** Construct a 95% confidence interval for the population mean estimated length of the vertical line.

**a.**

To determine

**To Find:** If the individuals in the sample significantly overestimate the true length of the line using one-tailed test with

Explanation

**Given info:**

A sample of 25 individual is selected from a population with mean 10. The sample mean, and standard deviation (s) are 12.2 and 1 respectively. One-tailed hypothesis test using

**Calculations:**

Step 1: Null Hypothesis is

Step 2: For a sample of

Step 3: t-statistics can be calculated using formula:

Calculate

**b.**

To determine

**To Find:** The Cohen’s d and

**b.**

To determine

**To Find:** Make a 95% confidence interval estimate for the given question

Essentials Of Statistics

Single Variable Calculus: Early Transcendentals, Volume I

Calculus (MindTap Course List)

Calculus: Early Transcendental Functions

Applied Calculus

Calculus: Early Transcendentals

Finite Mathematics and Applied Calculus (MindTap Course List)

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: An Applied Approach (MindTap Course List)

Multivariable Calculus

Statistics for The Behavioral Sciences (MindTap Course List)

Calculus (MindTap Course List)

Probability and Statistics for Engineering and the Sciences

Understanding Basic Statistics

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Intermediate Algebra

Finite Mathematics

Single Variable Calculus

Mathematical Excursions (MindTap Course List)

Elementary Technical Mathematics

Contemporary Mathematics for Business & Consumers

Mathematical Applications for the Management, Life, and Social Sciences

Elementary Geometry For College Students, 7e

Elements Of Modern Algebra

Single Variable Calculus: Early Transcendentals

Calculus: Early Transcendental Functions (MindTap Course List)

Trigonometry (MindTap Course List)

Calculus of a Single Variable

Introduction To Statistics And Data Analysis

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Study Guide for Stewart's Multivariable Calculus, 8th

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Geometry for College Students