Question

Sixty students were asked during finals week to choose their favorite treat to eat while studying. They were given four choices (cake, cookies, ice cream, donuts) and asked to choose one. Their data were as follows:

Cake 10

Cookies 12

Ice Cream 20

Donuts 18

Using an alpha of .05, conduct a hypothesis test by hand using all steps of hypothesis testing to examine the following research question: Is there a difference in students’ preferred choice of treat? Go through all of the steps in hypothesis testing including:

a) State your hypotheses.

b) Find the df and critical value(s)

c) Compute the test statistic by hand

d) Make a decision

e) Calculate effect size, if needed

f) Write your results sentence(s). Include your test statistic in journal form

Answer 1

(a)

H0: Null Hypothesis: There is no difference in students' preferred choice of treat.

HA: Alternative Hypothesis: There is difference in students' preferred choice of treat.

(b)

df = 4 - 1 = 3

= 0.05

From Table, critical value of = 7.8147

(c)

Assuming H0, the Expected Frequency of each choice = 60/4 = 15

Test statistic = is calculated as follows:

O	E	(O - E)2/E
10	15	1.6667
12	15	0.6
20	15	1.6667
18	15	0.6
Total = =		4.5334

So,

Test statistic = 4.5334

(d)

Since calculated value of = 4.5334 is less than critical value of = 7.8147, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that there is a difference in students' preference choice on treat.

(e)

Effect size need not be calculated because the difference is not significant.

(f)

Results:

In the Hypothesis Test of students' preference choice on treat: cake, cookies, ice cream, donuts, based on the data collected during finals week, the conclusion isthat there is no significant difference in students' preference choice on treat.