1. Why do the critical values from the Chi-square distribution get larger as the degrees of freedom get larger? Recall that this is opposite the pattern for the t-table.

2. Why is choosing sample size important(with specific reference to proportions)?

Solution Preview

Please see the attached Word document.

Sample size & Chi-square questions
1. Why do the critical values from the Chi-square distribution get larger as the degrees of freedom get larger? Recall that this is opposite the pattern for the t-table.

When we test a hypothesis that uses the Chi-square distribution as the reference distribution, the critical value is the value that "cuts off" a small area in the right tail of the distribution. It's a large percentile of the distribution, usually the 90th, 95th, or 99th percentile.
Chi-square is a family of distributions with many different members. Any particular member of the chi-square family of distributions is defined by a single ...

Solution Summary

The attached 400 word solution gives detailed explanations that discuss the sample size and chi-square questions.

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

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?

A chi-square test statistic was calculated to be 18, based on a sample variance of 20 and a hypothesized population variance of 40. How many observations were made when the sample was extracted? Which one?
a. 9
b. 10
c. 36
d. 37

A chi-square test for goodness of fit is used to test whether or not there are any preferences among three brands of cola. If the study uses a sample of n = 60 subjects, then the expected frequency for each category would be?

What are the four assumptions for the chi-square tests?
What are the hypothesis when conducting the chi-square tests for goodness-of-fit?
Why is there just one critical value for a chi-square test even when the hypothesis is a two-tailed test?

1. In a chi-square test, the sample data are called observed frequencies.
True
False
2. One advantage of the chi-square tests is that they can be used when the data are measured on a nominal scale.
True
False
3. A chi-square test for goodness of fit is used to evaluate a hypothesis

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?

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