   Chapter 15, Problem 5P 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

Research has demonstrated that people tend to be attracted to others who are similar to themselves. One study demonstrated that individuals are disproportionately more likely to marry those with surnames that begin with the same letter as their own (Jones, Pelham. Carvallo, & Mirenberg, 2004). The researchers began by looking at marriage records and recording the surname for each groom and the maiden name of each bride. From these records it is possible to calculate the probability of randomly matching a bride and a groom whose last names begin with the same letter. Suppose that this probability is only 6.5%. Next, a sample of n = 200 married couples is selected and the number who shared the same last initial at the time they were married is counted. The resulting observed frequencies are as follows: Same Initial Different Initials l 19 181 200 Do these data indicate that the number of couples with the some last initial is significantly different than would be expected if couples w ere matched randomly? Test with α = .05.

To determine
That the number of couples with the same last initials is significantly different than would be expected if couples were matched randomly.

Explanation

Given Info:

n=200andα=0.05

Calculation:

Given n=200,α=0.05

 Same initials Different initials 19 181 200

Step 1: Null hypothesis H0 is given as

H0: Null hypothesis indicates that the number of couples with same last initial is no significantly different from those couples who were randomly matched.

 Same initials Different initials 50% 50% 200

H1: There is significant difference in the sample chosen.

Step 2: Use α=0.05

For critical region the value of freedom is

df=C1=21=1

As df=1 and α=0.05, from the table of critical value of chi-square. Critical value of χ2 is 3

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