HW #10 STATs
In order to do a goodness-of-fit hypothesis test, the expected count in each cell must be at least ____.
5
In the special case in which both categorical variables have only two categories, the test of homogeneity is identical to which of the following?
A two-tailed z-test of two proportions
Which of the following is not a characteristic of the chi-square distribution?
Correct: The distribution is skewed left. Other options: The distribution allows for only positive values. The shape depends on a parameter called the degrees of freedom. The distribution is not symmetric.
The chi-squared statistic measures which of the following?
The amount by which the expected counts differ from the observed counts.
What area is used to compute the p-value for a chi-square test for goodness of fit?
The area to the right of the test statistic
The table shows the country of origin and the percentage of foreign-born people in a certain country in 2000 and 2007 for the four countries of origin with the highest percentages. Why should a chi-square test not be used with these data?
The data are of the entire population (not a sample), and therefore there is no need for inference. The data are given as rates (percentages), not frequencies (counts), and there is not enough information for us to convert these percentages to counts.
In a chi-square test for goodness of fit, which of the following is used to compute the degrees of freedom?
The number of categories for the variable minus 1
What are the expected counts in a two-way table?
The numbers of observations in each cell if the null hypothesis were true.
The shape of the chi-square distribution is ______.
The shape of the chi-square distribution is skewed right. The chi-square distribution is a right-skewed distribution. Next question
What is one drawback with chi-square tests?
The tests can reveal whether two variables are associated but not how they are associated.
For two or more samples and one categorical response variable, to determine if there is an association between categorical variables, a test of _________ is used.
homogeneity
If there is no association between the categorical variables, then which of the following must be true?
the observed counts in the two-way table should be close to the expected counts
A professor collected data from classes to see whether humans made selections randomly, as a random number generator would. Each of 41 students had to pick an integer from one to five. The data are summarized in the table below. A true random number generator would create roughly equal numbers of all five integers. Do a goodness-of-fit analysis to test the hypothesis that humans are not like random number generators. Use a significance level of α=0.05, and assume these data were from a random sample of students.
H0: Humans are like random number generators and produce numbers in equal quantities. Ha:Humans are not like random number generators and do not produce numbers in equal quantities. Choose chi-square goodness of fit (GOF). Note that the only variable is Integer Chosen. Use a significance level of 0.05. We are assuming randomness. There were 41 students. Check that all the expected counts are 5 or more. Since each expected count is 8.28.2, the condition that all the expected counts are 5 or more holds. Reject the null hypothesis. Humans have been shown to be different from random number generators.
For one sample and two categorical response variables, to determine if there is an association between categorical variables, a test of _______ is used.
independence
