Exam 15: Chi-Squared Tests Optional

In a goodness-of-fit test, all of the proportions specified in the null hypothesis must be equal to each other.

To produce expected values for a test of a contingency table, you multiply estimated joint probabilities for each cell by the total sample size, n.

A left-tailed area in the chi-squared distribution equals 0.10. For 5 degrees of freedom the table value equals 9.23635.

For comparing two or more populations each having two or more categories, you can use which test(s)?

If you want to describe a population with more than two categories, which test(s) can you use?

A chi-squared test of a contingency table is applied to a contingency table with 3 rows and 4 columns for two qualitative variables. The degrees of freedom for this test must be 12.

If we use the chi-squared method of analysis we must first check that there are at least 5 observations in each cell of the contingency table.

A chi-squared test of a contingency table with 6 degrees of freedom results in a test statistic $\chi$ ² = 13.58. Using the $\chi$ ² tables, the most accurate statement that can be made about the p-value for this test is that:

A chi-squared test of a contingency table with 10 degrees of freedom results in a test statistic of 17.894. Using the chi-squared table, the most accurate statement that can be made about the p-value for this test is that 0.05 < p-value < 0.10.

If you want to describe a population with two categories, you can use a(n) ____________________ test of p or the chi-squared goodness-of-fit test.

To determine whether a single coin is fair, the coin was tossed 200 times. The observed frequencies with which each of the two sides of the coin turned up are recorded as 112 heads and 88 tails. Is the coin fair?

If two events A and B are independent, the P(A and B) = P(A) + P(B).

Which of the following conditions indicate that H₀ should be rejected in a goodness-of-fit test?

The chi-squared test of a(n) ____________________ is used to determine whether there is enough evidence to say two nominal variables are related.

Suppose the value of your chi-squared test statistic in a goodness-of-fit test is equal to 0. What do you conclude?

For a chi-squared distributed random variable with 12 degrees of freedom and a level of significance of 0.05, the test statistics is 25.168. The chi-squared value from the table is 21.0261. These results will lead us to reject the null hypothesis.

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

If you want to compare two populations that each have two categories, you can use a z-test for two proportions, or a chi-squared test of a(n) ____________________.

The degrees of freedom for the test statistic in a test of a contingency table is (r - 1)(c -1) where r is the number of rows in the table, and c is the number of columns.

The following data are believed to have come from a normal probability distribution. 26 21 25 20 21 29 26 23 22 24 30 23 32 26 24 32 16 36 21 31 26 23 32 35 40 30 14 46 27 33 25 27 21 26 18 29 The mean of this sample equals 26.80, and the standard deviation equals 6.378. Use the goodness-of-fit test at the 5% significance level to test whether the data indeed come from a normal distribution.