Chi sqared test

Goodness of Fit

• A vending machine company claims the distribution of snack choices in their machines is 25% chips, 30% candy bars, 20% trail mix, and 25% cookies. An inventory audit reveals the counts differ. Use a .05 level of significance to test the claim that the snack distribution matches expectations.

Goodness of Fit

• A die manufacturer claims their dice are fair, meaning each face has an equal probability of rolling. A player tests this by rolling the die 120 times and recording the frequencies of each result. Use a .01 significance level to test whether the die is fair.

Goodness of Fit

• A wildlife organization claims the proportion of sightings for different bird species in a region follows a known distribution: 40% sparrows, 30% finches, 20% robins, and 10% hawks. Observed data is recorded in a table. Use a .05 significance level to test the claim that the proportions match.

Goodness of Fit

• A candy manufacturer claims that each color of jelly beans in their mix appears in the following proportions: 20% red, 20% green, 15% yellow, 15% orange, and 30% white. A large bag is analyzed, and the counts are recorded. Use a .1 significance level to test the claim that the proportions are as advertised.

Goodness of Fit

• A grocery store claims the distribution of purchases across categories—produce, dairy, meats, snacks, and beverages—matches their predictions. Sales data is recorded for a week. Use a .05 significance level to test whether the observed distribution matches the expected proportions.

Independence

• A study examines whether political party affiliation (Democrat, Republican, Independent) is independent of age group (18-29, 30-49, 50+). The survey results are recorded in a table. Use a .01 significance level to test the claim that age group and political party affiliation are not associated.

Independence

• A community group is curious to see if favorite outdoor activity (hiking, biking, swimming) is independent of gender. A survey collects responses and tallies results in a table. Use a .05 significance level to test the claim that gender does not influence outdoor activity preference.

Independence

• A hospital investigates whether the outcome of treatment (recovered, unchanged, worsened) is independent of the patient’s smoking status (smoker, non-smoker). Use a .01 significance level to test the claim that smoking status does not affect treatment outcomes.

Independence

• A study examines whether voting preferences in an election (Candidate A, Candidate B, Candidate C) are independent of ethnicity. Survey data is provided in a table. Use a .05 significance level to test the claim that ethnicity does not influence voting preferences.

Independence

• A car dealership investigates whether the preference for car color (red, black, white, blue) is independent of age group. Sales data for the month is recorded in a table. Use a .01 significance level to test the claim that car color preference is not related to age group.

Homogeneity

• A sports team’s coach wants to compare the training preferences (cardio, strength, endurance) across three teams: junior, senior, and professional. Data is collected for all players. Use a .05 significance level to test the claim that preferences are the same across teams.

Homogeneity

• A coffee shop chain analyzes whether customer preferences for beverage types (coffee, tea, smoothies) are consistent across three locations. Sales data is recorded in a table. Use a .01 significance level to test the claim that beverage preferences are consistent across all locations.

Homogeneity

• A school district investigates whether the proportions of students choosing science, math, or language arts as their favorite subject are the same across three schools. Survey results are summarized in a table. Use a .05 significance level to test the claim that the subject preferences are identical across schools.

Homogeneity

• A school district investigates whether the proportions of students choosing science, math, or language arts as their favorite subject are the same across three schools. Survey results are summarized in a table. Use a .05 significance level to test the claim that the subject preferences are identical across schools.

Homogeneity

11. A restaurant chain tests whether customer choices for menu categories (appetizers, entrees, desserts) are consistent across four locations. Observed frequencies are collected in a table. Use a .05 significance level to test the claim that menu preferences are consistent across all locations.