Chi Square Goodness of Fit

Given a significance level of 5%, should we accept or reject the null hypothesis.

• Since the p-value of 0.231 is greater than the significance level of 0.05, we should accept the null hypothesis.

• Since the p-value of 0.447 is greater than the significance level of 0.05, we should accept the null hypothesis.

• Since the p-value of 0.231 is less than the significance level of 5%, we should accept the null hypothesis.

• Since the p-value of 0.447 is greater than the significance level of 0.05, we should reject the null hypothesis.

What must be true about the expected values in a chi square test?

• greater than or equal to 2

• greater than or equal to 5

• greater than or equal to 10

• greater than or equal to 30

In both chi square tests, observed frequencies and expected frequencies are used to calculate the p-value

• True

• False

Python eggs How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother. Here are the data on the number of eggs that hatched and didn’t hatch. If the p-value is .08 and you use .05 as your alpha, what is your conclusion for the goodness of fit test.

• Fail to reject: We do not have sufficient evidence that distribution of hatched is different for water temperature options

• Reject: We do not have sufficient evidence that distribution of hatched is different for water temperature options

• Fail to reject: We do have sufficient evidence that distribution of hatched is different for water temperature options

• Reject: We do have sufficient evidence that distribution of hatched is different for water temperature options

What are the degrees of freedom for the following χ² test?

• 6

• 2

• 5

• 36

An individual wants to run a chi-squared goodness of fit test to determine how students in three different education settings (lecture, group work, individual online work) performed on an exam in terms of pass/fail. How many degrees of freedom would you require for this GOF test?

• 2

• 1

• 3

• 5

To verify large counts for any chi-squared test, we need to make sure our __________ counts are greater than ______.

• Expected, 5

• Observed, 5

• Expected, 10

• Observed, 10

The table shows the number or babies born on each day of the week. Is there evidence that births are more likely on specific days of the week? Use 5% level of significance.

• yes, the p value is greater than .05

• no, the p value is less than .05

• yes, the p value is less than .05

• no, the p value is greater than .05

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year. She wants to know if each type of food will be equally popular so she can start ordering supplies making other plans. To find out, she selects a random sample of 100 students and asks them, "Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?" Here are the data in the table provided. An appropriate null hypothesis to test whether the food choices are equally popular is:

• H₀: μ = 25, where μ = the mean number of students that prefer each type of food.

• H₀: p = 0.25, where p = the proportion of all students who prefer Asian food.

• H₀: η_A = η_M = η_P = η_H = 0.25, where η_A is the number of students in the school who would choose Asian food, and so on.

• H₀: p_A = p_M = p_P = p_H = 0.25, where p_A is the proportion of students in the sample who would choose Asian food, and so on.

Is there evidence that income levels are not evenly distributed across the entire population? What is the p value and chi square statistic?

• yes, p value is 2.42 e^-18, chi square statistic = 92.11

• yes, p value is .242, chi square statistic = 43.98

• no, p value is 2.42 e^-18, chi square statistic = 92.11

• no, p value is 2.42, chi square statistic = 43.98