An experimental psychologist plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a prestudy was designed in which participants were asked which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots. Do these scores suggest that the different foods are differentially preferred by people in general? (Use the .05 significance level.)
You must use all five steps in hypothesis testing:
Restate the question as a research hypothesis and a null hypothesis about the populations.
Determine the characteristics of the comparison distribution.
Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.
Determine your sample’s score on the comparison distribution.
Decide whether to reject the null hypothesis.

Answer:

Step-by-step explanation:

From the information given:

[tex]\mathbf{H_o: there \ is \ no \ significanr \ difference \ between \ observed \ and \ expected \ value }[/tex]

[tex]\mathbf{H_a: there \ is \ significanr \ difference \ between \ observed \ and \ expected \ value }[/tex]

The characteristic of the comparison is a uniform distribution.

Since there are three categories from the data, then: the data obeys a U(0,3) distribution. However, supposed it happened that different food had the same appeal, thus, there will be uniform distribution in the preference score.

[tex]Degree \ of \ freedom \ df = n - 1 \\ \\ df = 3 - 1 = 2[/tex]

At 0.05;

Thus, at 0.05 and df of 2, the cutoff sample score at which [tex]H_o[/tex] will be reject is the critical value [tex]\mathbf{X_{0.05,2}^2 \ which \ is \ = 5.991}[/tex]

Prefered     Observed    Expected     Expected     (O - E)       (O - E)²/ E

                   frequency   frequency     proportions

Cup cakes           16        20                  0.333          -4.00           0.800

Candy bars          26       20                 0.333             6.00           1.800

Dried apricots      18        20                 0.333            -2.00          0.200

Total                     60       20                     1                 -2.00           2.800

Thus the sample score is [tex]\mathbf{X^2_{observed} = 2.800}[/tex]

Decision rule: To reject the null hypothesis if the observed test statistic is higher than the critical value.

Conclusion: We fail to reject the null hypothesis and conclude that different foods have the same appeal to different people.

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