Do male and female children respond differently to colors? A study of color association in children asked separate random samples of male and female fourth-graders what emotion they associated with the color red. Here are the results for each group.

Under the assumption that the null hypothesis is true, which of the following represents the expected count for female children who associate the color red with love?

Is the accident rate for some car colors different than for other car colors? An insurance company selects a random sample of cars that it insures and records their color (using five categories: white, silver, black, red, or “all others”) and whether or not they have been involved in an accident in the last three years. They perform a chi-square test of association and obtain a test statistic of χ² = 8.474, which yields a P-value of 0.0757. Using a significance level of α = 0.05, which of the following is the appropriate conclusion for this test?

A well-known chewing gum maker wants to determine if any of its four flavors of gum are more popular than the others. A random sample of 80 people who say they chew gum regularly is asked to identify their favorite flavor of gum. Here are the results.

Which of the following are conditions that must be met in order to test this hypothesis using a chi-square test?

I. If p = proportion of gum-chewers in the population, then np ≥10 and n(1 - p) ≥ 10.

II. All expected cell counts are greater than 5.

III. The sample size of 80 is less than 10% of the targeted population.

A statistically-minded toll collector wonders if drivers are equally likely to choose each of the three lanes at his toll booth. He selects a random sample from all the cars that approach the booth when all three lanes are empty, so that the driver’s choice isn’t influenced by the cars already at the booth.

Here are his results:

A die was rolled 30 times with the following results:

A goodness-of-fit test is to be used to test the null hypothesis that the die is fair.  At a significance level of 1%, the value of the chi-square and the decision reached is

A company claims it audits its employees’ transactions based on their job level. For entry-level positions, the company claims that 50 percent get a basic audit, 30 percent get an enhanced audit, and 20 percent get a complete audit. The company tests this hypothesis using a random sample and finds χ² = 0.771 with a corresponding p-value of 0.68. Assuming that conditions for inference were met, which of the following is the correct interpretation of the p-value?