Chapter 10, Problem 19P

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Chapter
Section

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Numerous studies have found that males report higher self-esteem than females, especially for adolescents (Kling, Hyde, Showers. &. Buswell, 1999). Typical results show a mean self-esteem score of M = 39.0 with SS = 60.2 for a sample of n = 10 male adolescents and a mean of M = 35.4 with SS = 69.4 for a sample of n = 10 female adolescents.a. Do the results indicate that self-esteem is significantly higher for males? Use a one tailed lest with α = 01b. Use the data to make a 95% confidence interval estimate of the mean difference in self-esteem between male and female adolescents.c. Write a sentence demonstrating how the results from the hypothesis test and the confidence interval would appear in a research report.

a.

To determine

To check: Whether the self-esteem is significantly higher for males using one-tailed test with α=0.01

Explanation

Given info:

Two sample each with size 10 has means 39 and 35.4 respectively. The sum of squared difference (SS) for two samples is 60.2 and 69.4 respectively.

Calculations:

Step 1: Null hypothesis is H0:μ1μ20, alternate hypothesis is H1:μ1μ2>0.

Step 2: For the given sample, degrees of freedom is

df=n1+n22=10+102=18

For on tailed test with α=0.01 and df=18, the critical value (CV) is obtained from t-table as t=2.552

Step 3: t-statistics is calculated using formula

t=M1M2(μ1μ2)sM1M2

Pooled variance, sp2:

sp2=SS1+SS2df+df2=60

b.

To determine

To compute: The 95% confidence interval for the given question.

c.

To determine

To writhe: The outcome of study as it appears in the final report.

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