Unit 8: Inference for Categorical Data: Chi-Square

The chi-square test statistic is computed as:

A chi-square test for independence tests whether:

The expected count for a cell in a two-way table under the null hypothesis of independence is:

The Large Counts condition for a chi-square test requires:

The degrees of freedom for a chi-square test for independence with a table having [math] rows and [math] columns is:

Which cell contributes most to the chi-square statistic?

The degrees of freedom for a chi-square goodness-of-fit test with [math] categories is:

A large chi-square statistic provides evidence:

A 95% confidence interval for a population mean is (42, 58). Which of the following is the correct interpretation?

A poll of 400 voters finds 55% support a candidate with a margin of error of ±3%. Which interval estimates the true proportion?

To cut the margin of error of a confidence interval in half, the sample size must be:

For a 99% confidence interval using the z-distribution, the critical value z* is approximately:

In a random sample of 200 adults, 120 approve of a policy. What is the 95% confidence interval for the true proportion?

Compared to a z-interval, a t-interval with the same confidence level and sample size is:

Which condition is required to construct a confidence interval for a population mean using a t-distribution?

If you increase the confidence level from 90% to 99%, what happens to the width of the confidence interval?

A researcher wants a 95% CI for a proportion with margin of error no more than 0.03. Using p̂ = 0.5, what is the minimum sample size?

A 95% confidence interval for μ₁ − μ₂ is (−3, 7). What can we conclude?

What is the expected count for each color if the company's claim is true?

What is the chi-square test statistic?