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?

What is the expected count for the cell "Male and Dog"?

What conclusion should be reached?

Which condition must be checked before performing a chi-square test?

What are the degrees of freedom for this chi-square test of independence?

Is this a test of independence or homogeneity?

Which cell contributes the most to the chi-square statistic?

A biologist crosses two pea plants and expects offspring colors in a 9:3:3:1 ratio. Of 160 offspring observed: 85 yellow-round, 30 yellow-wrinkled, 34 green-round, and 11 green-wrinkled. Expected counts are 90, 30, 30, and 10. χ² = 0.278 + 0 + 0.533 + 0.1 = 0.911 with df = 3. What is the appropriate conclusion at α = 0.05?

A researcher surveys 300 adults and records their preferred news source (TV, Online, Print) and age group (Under 40, 40 and over). To test whether news source preference is associated with age group, which test should be used and why?

In a chi-square test, one cell has an expected count of 3.2. A student proceeds with the test. What concern does this raise?

A polling agency surveys voters in three cities to see if the proportion supporting a tax increase differs among cities. The data are: City A (120 yes, 80 no), City B (90 yes, 110 no), City C (95 yes, 105 no). Which test is appropriate?

A chi-square goodness-of-fit test with 4 categories yields χ² = 9.35. With α = 0.05 and df = 3, the critical value is 7.815. What is the appropriate conclusion?