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Essentials of Statistics for the B...

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

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BuyFindarrow_forward

Essentials of Statistics for the B...

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

A researcher uses a matched-subjects design to investigate whether single people with pets are happier than singles without pets. A mood inventory survey is given to a group of 20- to 29-year-old non-pet owners and a similar age group of pet owners. The pet owners are matched one to one with the non-pet owners for income, number of close friendships, and general health. The data follow:

  images

a. Is there a significant difference in the mood scores for non-pet owners versus pet owners? Test with α = .05 for two tails.

  b Construct the 95% confidence interval to estimate the size of the mean difference in mood between the population of pet owners and the population of non-per owners, (You should find that a mean difference of μ D = 0 is an acceptable value, which is consistent with the conclusion from the hypothesis test.)

a.

To determine
Whether there is a significant difference between the mood scores for non-pet owners and pet owners.

Explanation

Given info:

The given data are shown below,

Matched pair Non pet owner Pet owner
A 12 14
B 8 7
C 10 13
D 9 9
E 7 13
F 10 12

Calculation:

The difference D, D and D2 is obtained below:

Participants White background Red background D D2
A 12 14 2 4
B 8 7 –1 1
C 10 13 3 9
D 9 9 0 0
E 7 13 6 36
F 10 12 2 4
Total     12 54

Thus, the values of D is 14 and D2 is 54.

The mean difference MD:

MD=DN=126=2

Thus, the mean difference MD is 2.

The value of SS is,

SS=D2(D)2N=541446=5424=30

Thus, the value of SS is 30

b.

To determine
The confidence interval to estimate the mood difference at 95 %.

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