Question

Conditions Explain why it is not safe to use the methods of this chapter to perform inference in each of the following settings.

(a) Lyme disease is spread in the northeastern United States by infected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected ticks. The mouse population in turn rises and falls with the abundance of acorns, their favored food. Experimenters studied two similar forest areas in a year when the acorn crop failed. They added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched.

The next spring, $54$of the $72$mice trapped in the first area were in breeding condition, versus $10$of the $17$mice trapped in the second area.50

(b) Who texts more—males or females? For their final project, a group of AP Statistics students investigated their belief that females text more than males. They asked a random sample of $31$students—$15$males and $16$females—from their school to record the number of text messages sent and received over a two-day period. Boxplots of their data are shown below

Short answer

a). Normal requirement has not been met.

b). Normal requirement is not met.

Step-by-step solution

Part (a) Step 1: Given Information

The next spring, $54$of the $72$mice trapped in the first area were in breeding condition, versus $10$of the $17$ mice trapped in the second area.

Part (a) Step 2: Explanation

Three conditions if using the inference procedure of this chapter are random, independent and normal. The normal requirement for differentiating two proportions is that the number is not success and success is at least $10$for the both of the samples. It is observed that this requirement is not satisfied, the reason is that the second sample is having $10$successes out of $17$ and therefore also $7$ failures (less than $7$ ).

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

Three conditions if using the inference procedure of this chapter are random, independent and normal. The normal requirement for differentiating two means is that the sample distribution is about normal and having no outlier. It is observed that this requirement is not satisfied, the reason is that the males' sample is having $2$ outliers which is indicated by the two dots in the box plot.