Exam 15: Chi-Squared Tests Optional

Consider a multinomial experiment with 200 trials, where the outcome of each trial is classified into one of 5 categories. The number of degrees of freedom associated with the chi-squared goodness-of-fit test equals:

If the observed frequencies are all smaller than the expected frequencies in a goodness-of-fit test, the chi-squared test statistic will be negative.

If you want to describe a population with more than two categories, you can use a chi-squared ____________________ test.

How do you calculate the expected frequency for one cell in a goodness-of-fit test?

NARRBEGIN: Students Absenteeism Student Absenteeism Consider a multinomial experiment involving n = 200 students of a large high school. The attendance department recorded the number of students who were absent during the weekdays. The null hypothesis to be tested is: H₀: p₁ = 0.10, p₂ = 0.25, p₃ = 0.30, p₄ = 0.20, p₅ = 0.15.NARREND -{Student Absenteeism Narrative} Review the previous results. What is the effect of decreasing the sample size?

Five types of apples are displayed side by side in several supermarkets in the city of Miami. It was noted that in one day, 180 customers purchased apples. Of these, 30 picked type A, 40 picked type B, 25 picked type C, 35 picked type D, and 50 picked type E. In Miami, can you conclude at the 5% significance level that there is a preferred type of apples?

In the test of a contingency table, the observed cell frequencies must satisfy the rule of 5.

In 2011, the student body of a state university in Alabama consists of 30% freshmen, 25% sophomores, 27% juniors, and 18% seniors. A sample of 400 students taken from the 2012 student body showed that there are 138 freshmen, 88 sophomores, 94 juniors, and 80 seniors. Test with 5% significance level to determine whether the student body proportions have changed.

Explain what is meant by the rule of five and what you should do if this rule is not met.

If we want to perform a two-tail test of a population proportion p, we can only use the z-test of p.

The total of the observed frequencies in a multinomial experiment must equal nk where n is the number of trials and k is the number of categories.

You find the expected value for each cell in a chi-squared test for a contingency table by multiplying the ____________________ total by the ____________________ total and dividing by the sample size, n.

NARRBEGIN: Seat Belts Seat Belts A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car. A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident. The data are shown in the table below. Child present in car Seat Belts NO YES Worn 83 200 Not Worn 337 380 NARREND -{Seat Belts Narrative} State the appropriate null and alternative hypotheses for this experiment.

A cable company prepared four versions of a set of instructions for hooking up a TV. The company asked a sample of 1,600 people which one of the four forms was easiest to understand. In the sample, 425 people preferred Form A, 385 preferred Form B, 375 preferred Form C, and 415 preferred Form D. At the 5% level of significance, can one conclude that in the population there is a preferred form?

When k = 2 the ____________________ experiment is identical to the ____________________ experiment.