Chapter 10.4, Problem 1LC

BuyFind*arrow_forward*

8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

A researcher is using an independent-measures design to evaluate the difference between two treatment conditions with *n* = 8 in each treatment. The first treatment produces *M* = 63 with a variance of *s*^{2} = 18, and the second treatment has *M* = 58 with *s*^{2} = 14.

a. Use a one-tailed test with
*Note:* Because the two samples are the same size, the pooled variance is simply the average of the two sample variances.)

b. Predict how the value for the *t* statistic would be affected if the two sample variances were increased to *s*^{2} = 68 and *s*^{2} = 60. Compute the new *t* to confirm your answer.

c. Predict how the value for the *t* statistic for the original samples would be affected if each sample had *n* = 32 scores (instead of *n* = 8). Compute the new *t* to confirm your answer.

**a.**

To determine

Whether the scores in the first treatment significantly greater than the scores in the second treatment.

Explanation

**Given info:**

Two samples each of size 8 has means 63 and 58 respectively. The variances for the two samples are 18 and 14 respectively.

**Calculation:**

Step 1: Null hypothesis is

Alternate hypothesis is

Step 2: For the given sample, t-statistics will have degree of freedom equals:

For one-tailed test with

Step 3: t-statistics is obtained as below,

*Pooled variance*
*:*

Where,

*Ss _{2}:*

**b.**

To determine

**To predict:** The effect of the value in *t-*statistic if the two sample variances are increased.

**To compute**: The new t.

**c.**

To determine

**To predict:** The effect of the value in *t-*statistic if the values of sample sizes increased to 32.

**To determine**: Whether the above prediction is correct or not by finding the t value.

Essentials Of Statistics

Statistics for The Behavioral Sciences (MindTap Course List)

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Probability and Statistics for Engineering and the Sciences

Understanding Basic Statistics

Elements Of Modern Algebra

Finite Mathematics

Calculus (MindTap Course List)

Contemporary Mathematics for Business & Consumers

Calculus of a Single Variable

Calculus (MindTap Course List)

Calculus: Early Transcendentals

Intermediate Algebra

Calculus: An Applied Approach (MindTap Course List)

Precalculus: Mathematics for Calculus (Standalone Book)

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Technical Mathematics

Calculus: Early Transcendental Functions

Trigonometry (MindTap Course List)

Finite Mathematics and Applied Calculus (MindTap Course List)

Single Variable Calculus: Early Transcendentals, Volume I

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

Mathematical Excursions (MindTap Course List)

Applied Calculus

Elementary Geometry For College Students, 7e

Multivariable Calculus

Calculus: Early Transcendental Functions (MindTap Course List)

Mathematical Applications for the Management, Life, and Social Sciences

Single Variable Calculus: Early Transcendentals

Single Variable Calculus

Introduction To Statistics And Data Analysis

Study Guide for Stewart's Multivariable Calculus, 8th

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

Elementary Geometry for College Students