Chi-Square Goodness of Fit Test

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.  The P-value for a chi-square test for goodness of fit is 0.0129.  Which is the following is the most appropriate conclusion?

• Because 0.0129 is less than α = 0.05, reject H₀.  There is convincing evidence that the food choices are equally popular.
• Because 0.0129 is less than α = 0.05, reject H₀.  There is not convincing evidence that the food choices are equally popular.
• Because 0.0129 is less than α = 0.05, reject H₀.  There is convincing evidence that the food choices are not equally popular.
• Because 0.0129 is less than α = 0.05, fail to reject H₀.  There is convincing evidence that the food choices are equally popular.

Aw, nuts! A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts from the latest batch. The one-way table below displays the sample data. What is the appropriate null hypothesis for this goodness of fit test.

• p₁=p₂=p₃=p₄

• Mixed nut proportions are proportioned the same as they claim

• At least one of the four types in the population is different than expect

• the observed counts are equally distributed

How do you find degrees of freedom for a chi-square goodness of fit test?

• one less than the number of categories

• one less than the population size

• one less than the sample size

• two less than the sample size

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?

• yes, the p value is greater than .05

• no evidence, the p value is less than .05

• yes, the p value is less than .05

• no evidence, the p value is greater than .05

The bigger the chi square statistic, the ________ the p value.

• bigger
• smaller

How many degrees of freedom will be present?

• 4

• 5

• 6

• 7

For any hypothesis test, which of the following conditions would lead you to reject the null hypothesis and accept the alternative?

• The calculated p-value is less than the significance level of the test

• The calculated p-value is less than the critical value

• The calculated test statistic is less than the significance level of the test

• The calculated test statistic is less than the critical value

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

• True

• False

The chi squared test is used to compare the means between two or more populations.

• True

• False

Use a goodness of fit test to determine if high school principals believe that students are absent equally during the week or not.

• True

• False