A researcher wants to identify three types of food reward that would be equal in

Question

A researcher wants to identify three types of food reward that would be equal in their appeal so that she can use them in a future study. After some research, the researcher found three food rewards that should be comparable in appeal. That is, her “expectation” is that roughly the same number of people would pick each food reward to be their favorite. Before adopting these three food items, however, she would like to formally test them with some real data. So she recruited 60 participants and asked them which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots. Conduct a Chi-Square Test for Goodness of Fit using a .05 significance level.

State the null and alternative hypotheses in words (1 point each, 2 points total)

Calculate X2 statistic (1 for formula, 1 for process, 1 for result, 3 points total)

Identify the critical value (1 point)

Compare the X2 statistic with the critical value (1 point)

Make a decision about the hypothesis test, using “reject” or “fail to reject” in the answer (1 point)

Explain the conclusion in a sentence or two (1 point)

Explanation / Answer

null hypothesis: choice of food items are independent of food items

alternate hypothesis:they are dependent on food item

from above X2 stat= 2.80

here degree of freedom =3-1=2

for above at 0.05 level, critical value of X2 =5.9915

as chi stat is lower then critcal value of chi sqaure we fail to reject null hypothesis.

hence we can accept that that roughly the same number of people would pick each food reward to be their favorite

observed Expected Chi square design P O E=total*p =(O-E)^2/E cupcakes 1/3 16 20 0.80 candy bars 1/3 26 20 1.80 dried apricots 1/3 18 20 0.20 total 60 60 2.80

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