   Chapter 15, Problem 4RE 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

A communications company has developed three new designs for a cell phone. To evaluate consumer response, a sample of 60 college students and 60 older adults is selected and each person is given all three phones to use for I week. At the end of the week, the participants must identify which of the three designs they prefer. The distribution of preference is as follows:   Design 1 Design 2 Design 3   Student 27 20 13 60 Older Adult 21 34 5 60   48 54 18   a. Do the data indicate that the distribution of preferences for older adults is significantly different from the distribution for college students’ Test with α = .05. b. Compute the phi-coefficient to measure the strength of the relationship.

a.

To determine

To test: Whether there is any significant difference between the distribution of preferences for older adults and thedistribution of preferences for college students.

Explanation

Given info:

A sample of 60 students and 60 adults is selected to identify the preference among the cellphone designs (3 designs) provided. Use α=0.05 to test the claim.

Calculation:

The test hypotheses are given below:

Null Hypothesis:

H0: There is no significant difference between the distribution of preferences for older adults and the distribution of preference for college students.

Alternate Hypothesis:

H1: There is a significant difference between the distribution of preferences for older adults and the distribution of preference for college students.

Degrees of freedom:

The degrees of freedom is,

R equals number of rows and C equals columns

df=(R1)(C1)   =(21)(31)=2

Thus, the degree of freedom is 2.

Critical value:

From the chi-square tabulated values, the critical value that corresponds to α=0.05 and df=2  is 5.991.

Test statistic:

The χ2statistics is,

χ2=(fofe)2fe

The formula to calculate expected frequency is:

fe=fcfrn...where fr is row frequency and fc is column frequency

Substitute n=120 in the above formula and compute respective values of expected frequencies:

For students, the expected frequencies are:

fe,design1=48×60120=24fe,design2=54×60120=27fe,design3=18×60120

b.

To determine

To Find: The phi-coefficient to measure the strength of relationship.

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