Question

A large middle school administrator wishes to use celebrity influence to encourage students to make healthier choices in the school cafeteria. The cafeteria is situated at the centre of an open space. Every day at lunch time students get their lunch and a drink in three separate lines leading to three separate serving stations. As an experiment, the school administrator displayed a poster of a popular teen pop star drinking milk at each of the three areas where drinks are provided, except the milk in the poster is different at each location: one shows white milk, one shows strawberry-flavoured pink milk, and one shows chocolate milk. After the first day of the experiment the administrator noted the students’ milk choices separately for the three lines.

The data are given in the table provided.
Student choice
Poster Choice l Regular l Strawberry l Chocolate l
Regular l 38 l 28 l 40
Strawberry l 18 l 51 l 24
Chocolate l 32 l 32 l 53

Formulate the appropriate null and alternative hypothesis in this context.
Which statistical test will you advise in this scenario?
Test, at the 1% level of significance, whether there is sufficient evidence in the data to conclude that the posters had some impact on the students’ drink choices.

Answer 1

The appropriate null and alternative hypotheses in this context can be formulated as follows:

Null hypothesis (H0): The posters have no impact on the students' drink choices. The proportions of students choosing each type of milk (regular, strawberry, and chocolate) are equal in all three lines.

Alternative hypothesis (Ha): The posters have an impact on the students' drink choices. The proportions of students choosing each type of milk are not equal in all three lines.

To test this hypothesis, we can use the chi-square test for independence. This test determines whether there is a relationship between two categorical variables (in this case, the poster choice and the drink choice) in a sample.

The chi-square test will allow us to determine if there is sufficient evidence in the data to conclude that the posters had some impact on the students' drink choices.

To perform the chi-square test, we need to set the significance level, which is given as 1% in this scenario. This means that we want to be 99% confident in our conclusions.

By calculating the chi-square statistic and comparing it to the critical value from the chi-square distribution table, we can determine if the difference in drink choices across the different poster choices is statistically significant or simply due to random chance.

If the calculated chi-square statistic is greater than the critical value, we can reject the null hypothesis and conclude that there is evidence of an association between the posters and the students' drink choices. If the calculated chi-square statistic is less than the critical value, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest an association.

In summary, the appropriate statistical test to use in this scenario is the chi-square test for independence. This test will allow us to analyze the relationship between the posters and the students' drink choices and determine if there is sufficient evidence to conclude that the posters had some impact.