   Chapter 15, Problem 3RE 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 developmental psychologist would like to determine whether infant , display any color preferences. A stimulus consisting of four color patches (red. green, blue, and yellow) is projected onto the ceiling above a crib. Infants are placed in the crib, one at a time, and the psychologist records how much time each infant spends looking at each of the four colors. The color that receives the most attention during a 100-second test period n identified as the preferred color for that infant. The preferred colors for a sample of 60 infants are shown in the following table: Red Green Blue Yellow 20 12 18 10 a. Do the data indicate any significant preferences among the four colors? Test at the .05 level of significance. b. Write a sentence demonstrating how the outcome of the hypothesis test would appear in a research report.

a.

To determine

To Find: Is their significant preferencesamong the four colors at α=0.05

Explanation

Given info:

The data represents the colour preference for a sample of 60 infants and the level of significance is α=0.05.

Calculations:

The test hypotheses are given below:

Null Hypothesis:

H0: There is no significant preference for the four colours.

Alternate Hypothesis:

H1: There is a significant preference for the four colours.

Degrees of freedom:

The degrees of freedom is,

df=(C1)   where C equals number of categories=41=3

Thus, the degree of freedom is 3.

Critical value:

From the Chi-square tabulated value the critical value that corresponds to α=0.05 and df=3 is 7.815.

Test statistic:

The χ2statistics is,

χ2=(fofe)2fe

Hypothetically, the proportion of each colour should be 0.25 each.

The formula to calculate expected frequency is:

fe=p×n

Substituting respective values of proportion and n=80 in the above formula:

fe,red=0.20×60=12fe,blue=0

b.

To determine

To explain: The outcome of hypothesis in correspondence to the report.

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