   Chapter 9, Problem 13P Essentials of Statistics for the B...

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

Solutions

Chapter
Section Essentials of Statistics for the B...

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

Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was μ = 15.1. A sample of n = 16 of today’s children produces a mean score of M = 23.3 with SS – 240.a. Based on the sample, has there been a significant change in the average level of anxiety since the 1950s? Use a two-tailed test with α = .01.b. Make a 90% confidence interval estimate of today’s population mean level of anxiety.c. Write a sentence that demonstrates how the outcome of the hypothesis test and the confidence interval would appear in a research report.

a.

To determine

To Find: If there has been a significant change in the average level of anxiety since 1950 using two-tailed test with α=0.01 .

Explanation

Given info:

A sample of 16 today’s children are selected from a population with mean 15.1. The sample mean, and sum of squared difference (SS) is found to be 23.3 and 240 respectively. Two-tailed hypothesis test using α=0.01 is to be performed.

Calculations:

Step 1: Null Hypothesis is H0:μ=15.1 and Alternate Hypothesis is H1:μ15.1

Step 2: For a sample of n=16 , the t-statistics will have (n1) degrees of freedom, i.e. df=15 . For a two-tailed test with α=0.01 and df=15 , the critical value (CV)  is obtained from the t-table as t=±2.947 .

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

t=Mμsm

Calculate sm using the formula:

sm=SSn(n1)=24016×15=240240=1

Now, substitute 23

b.

To determine

To Find: Make a 90% confidence interval estimate for the given question

c.

To determine

To State: How would the outcome of hypothesis test and confidence interval will appear in the research report.

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