(1) In a contingency table a sample of 400 people is classified by gender and hair color (4 groups: blond, brown, black, and red). How many degrees of freedom are there?

A. 3
B. 8
C. 399
D. None of the above.

(2) To find the expected frequency in a contingency table

A. Take the square root of the degrees of freedom.
B. Multiply the row and column totals and divide by the grand total.
C. Use the total number of observations minus one.
D. None of these.

(3) Suppose we are conducting a Chi-Square Goodness of Fit test of hypothesis to determine if a set of observations with 6 categories meets an expected set. How many degrees of freedom are there?

A. 5
B. 97
C. 3
D. None of these

(4) Under what conditions could the Chi-square distribution assume negative values?

A. When the sample size is small.
B. When the cell frequencies are all equal.
C. When the degrees of freedom is 1.
D. Never

Solution Preview

(1) In a contingency table a sample of 400 people is classified by gender and hair color (4 groups: blond, brown, black, and red). How many degrees of freedom are there?

The degrees of freedom equals the number of rows - 1 multiplied by the number of columns - 1. ...

In a test of the independence of two variables, one the variables has two possible categories and the other has three possible categories. What will be the critical value of chi-square if the test is to be carried out at the 0.025 level? At the 0.05 level?

Is there an alternative test to the chi squared test? What if my results give an expected frequency below 5, which stats book states that these should be treated with caution? Is there a more appropriate stat test which would be more accurate in working out the significance of the results?

You run a chi-square test. The critical value for this test at the .05 level is a chi-square of 6.21. What value must your obtained chi square
statistic be in order to be considered significant at the .05 level?

a) Why do you use the chi-square statistic?
b) What type of data is used with chi square analysis?
c) What are the hypotheses in a chi-square test for independence?
d) How do we calculate the expected frequencies for each cell of a contingency table?
e) How do we calculate the degrees of freedom for an r x c contingency

What happens to the shape of the Chi Square distribution curve as the sample size gets larger? What about when the number of cells or groups gets larger?

Cross between pure red tomato and yellow tomato produced all red F1 progeny. From the F2 progeny of 400 plants, 90 were yellow. Hypothesize that a single pair of allele is involved such that Y- = Red and yy = Yellow. Test this hypothesis using Chi square test.

A) When will you use a Goodness-of-fit Chi-Square distribution?
b) What are the characteristics of chi-square distribution?
c) Do you have to follow the five step process of hypothesis testing?
d) What are the drawbacks of chi-square testing?

A research organization has collected the following data on household size and telephone ownership for 200 U.S. households at the 0.05 level, are the two variables independent? Based on the chi-square table, what is the most accurate statement that can be made about the p-value for the test?

Please provide steps to solve the following question.
A study is designed to investigate whether there is a difference in response to various treatments I patients with chronic pain. The data are shown below. Are symptoms independent of treatment? Conduct a chi square test at a 5% level of significance.
Df = ?
Critical val

A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that:
a. p-value < 0.01
b. 0.025 > p-value > 0.01
c. 0.05 > p-value > 0.025
d. 0.10 > p-value > 0.05