Question

A researcher surveyed three groups of people below and recorded their preference for ice cream.
Do a chi square test to see if the proportions are the same for flavor preference for all three groups.

	Chocolate	Vanilla	Neither
Children	40	22	18
Teens	22	23	35
Adults	31	34	15

a) Write the expected value for each cell in parentheses in each cell.
b) Write the null and alternative hypotheses.
c) Find the critical value of Chi-Square for a : 0.05
d) Find the test value for Chi-Square.

e) What is the decision?
0 Summary statement:

Answer 1

The expected frequencies are -

Expected Values	Chocolate	vanilla	Total
Child	\frac{ 93 \times 62}{ 172} = 33.52317293×62​=33.523	\frac{ 79 \times 62}{ 172} = 28.47717279×62​=28.477	62
teens	\frac{ 93 \times 45}{ 172} = 24.33117293×45​=24.331	\frac{ 79 \times 45}{ 172} = 20.66917279×45​=20.669	45
adults	\frac{ 93 \times 65}{ 172} = 35.14517293×65​=35.145	\frac{ 79 \times 65}{ 172} = 29.85517279×65​=29.855	65
Total	93	79	172

Based on the observed and expected values, the squared distances can be hit like please.