Question

The chi-square test for homogeneity. In a study of the snack preferences of children, a marketing firm selects a random sample of 90 children under 8, 150 children aged 8-10,55 kids aged 11-13 and 50 kids aged 14-17. Each individual is asked which of the following snacks they prefer: Doritos, Ruffles, or Cheetos. Results are shown in the contingency table below. Total Snack Preferences Ruffles Doritos Cheetos 40 30 20 90 60 40 150 Under 8 Age 8-10 Age 11-13 Age 14-17 Total 50 20 10 25 10 55 30 50 10 125 120 100 345 6. Explain what makes this a stratified random sample: 7. What groups are being compared? 8. What is the variable of interest? 9. Do the proportions that prefer each type of snack differ significantly between each age group? Use a 0.05 level of significance. For Step 3, use http://www.quantpsy.org/chisq/chisq. htm

Answer 1

Answer(6):

Since, the whole population of children has been divided into different stratums with stratifying factor as age of children exmaple: the age group of under 8 children, between 8 to 10 etc. After which the sampling has been done at random from different stratums. Hence, the method of sample selection adopted is stratified random sampling.

"In a layman's language, when the population is divided into smaller sub-groups on the basis of a shared attribute, and then simple random sampling is employed separately to each of the strata, this procedure of sample selection is called Stratified Random Sampling."

Answer(7):

There are three groups in consideration:

1. Children who prefer Doritos in their snacks

2.Children who prefer Ruffles in their snacks

3.Children who prefer Cheetos in their snacks

These three groups are being compared.

Answer(8):

There are two variables of interest in a Chi-sqaure test, categroies of one is measured across the categories of second. Here, they are:

1. No of children belonging to different age groups

2. No of children preferring a particular type of snacks

Answer(9):

The hypotheiss are:

Null Hypothesis: Proportions of children preferring different snacks do not differ significantly across various age groups.

Alternative Hypothesis: Proportions of children preferring different snacks differ significantly across various age groups.

Using Chi-square test, the values are:

Chi-Square: 31.917

Degree of freedom: 6

p-value: 0.00001693

Decision: Since, p-value << ( $\alpha$ =0.05). Hence, we have sufficient evidence to reject the null hypothesis.

Conclusion: Hence, the children preferring different snacks vary in accordance with the age group they are related.