Exam 15: Chi-Squared Tests

You cannot use a chi-squared goodness-of-fit test when there are only two possible outcomes for each trial in your experiment.

The alternative hypothesis in a goodness-of-fit test is that none of the p_i values are equal to their values specified in H₀.

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 expected cell frequencies must satisfy the rule of 5.

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Child present in car Seat Belts NO YES Worm 83 200 Not Worn 337 380 -{Seat Belts Narrative} State the appropriate null and alternative hypotheses for this experiment.

Conduct a test to determine whether the two classifications A and B are independent,using the data in the accompanying table and $\alpha$ = .05. 35 25 20 25 20 25

To calculate the expected values in a test of a contingency table,you assume that the null hypothesis is true.

Suppose that two shipping companies,A and B,each decide to estimate the annual percentage of shipments on which a $100 or greater claim for loss or damage was filed by sampling their records,and they report the data shown below. Company A Company B Total shipments sampled 800 600 Number af shipments with a clain \geq\ 100 200 100 The owner of Company B is hoping to use these data to show that her company is superior to Company A with regard to the percentage of claims filed.Which test would be used to properly analyze the data in this experiment?

Which of the following represents H₁ in a chi-squared goodness-of-fit test to see if all 5 colors of a certain candy appear in the same proportion in the population?

The rule of five requires that the:

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

In a chi-squared test of a contingency table,the value of the test statistic was $\chi$ ² = 15.652,and the critical value at $\alpha$ = .025 was 11.1433.Thus,we must reject the null hypothesis at $\alpha$ = .025.

The null hypothesis in a chi-squared test of a contingency table is that the two nominal variables are ____________________.

The rule of five states that in order to conduct the chi-squared goodness-of-fit test,the ____________________ value for each cell must be five or more.

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.

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

Which of the following tests is appropriate for nominal data if the problem objective is to describe a population with more than two categories?

The chi-squared test for normality must follow the rule of ____________________ regarding expected values.

A chi-squared test of a contingency table can be used to determine whether two nominal variables are ____________________.

We can use the goodness-of-fit test to determine whether data were drawn from any distribution of interest.The most common application of this procedure is a test of ____________________.