Question

1) A researcher 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.)

In Step 1 of hypothesis testing, what is the null hypothesis?

1 - The frequency of people in all category are all the same

2 - The frequency of people across categories are not the same
3 - The distribution of numbers of people over categories varies
4 - The category for preferred candy bars has more participants than any other
5 - The category for preferred candy bars does not have more participants than any other
6 - The distribution for preferred candy bars is normal

2) In the study above, what is the cutoff sample score at which the null hypothesis should be rejected? (use the 3 decimal places)

3)When you determined the cutoff sample score above, what degrees of freedom did you use?

4) In the study above, what is E for any given category?

5) In the study above, what is χ²? (Round off answer to 1 decimal point)

Answer 1

1)Here null hypothesis is: The frequency of people in all category are all the same

2)The cutoff sample score at which the null hypothesis should be rejected is 0.05 which is the significance level

3)degree of freedom is n-1 means total type of categories i.e 3-1=2

4)Expected value for each category E is 60/3=20

5)Cupcakes observed 16 expected 20 (O-E)^2/E=0.8

Candy bars observed frequency 26 Expected 20 (O-E)^2/E=1.8

Dried apricots Observed frequency 18 Expected 20 (O-E)^2/E=0.2

Sum of (O-E)^2/E=0.8+1.8+0.2=2.8

Chi-square statistic X^2=Sum of (Observed frequency-Expected frequency)^2/expected frequency=2.8

Here P-value for the Chi-test=0.246

As P-value(0.246) is greater that the alpha(0.05) we fail to reject the null hypothesis.

So we do not have sufficient evidence to suggest the claim that that the different foods are differently preferred by people in general