Question

Question:

A group of health researchers survey a SRS of 300 teenagers, of whom 120 have low weekly outdoor activity levels and 180 have high weekly outdoor activity levels. Suppose that 35 percent of teenagers with low outdoor activity levels have allergies, and that 41 percent of teenagers with high outdoor activity levels have allergies. The researchers want to see the difference between the sample proportions. What will be the shape of the sampling distribution be and why?

Choices:
A. Approximately normal, because we expect 105 successes and 195 failures from teenagers with low levels, and 123 and 177 from teenagers with high levels, and all of these counts are at least 10.
B. Approximately normal, because we expect 42 successes and 78 failures from teenagers with low levels, and 73.8 and 106.2 from teenagers with high levels, and all of these counts are at least 10.
C. Not normal, because we expect fewer than 10 failures in both samples.
D. Not normal, because we expect fewer than 10 successes in both samples.

Answer 1

The shape of the sampling distribution will be B. Approximately normal, because we expect 42 successes and 78 failures from teenagers with low levels, and 73.8 and 106.2 from teenagers with high levels, and all of these counts are at least 10.

Step-by-step explanation:

The shape of the sampling distribution will be approximately normal because all the counts in the sample are at least 10.

In the low outdoor activity group, we expect 120 x 0.35 = 42 successes (allergies) and 120 x 0.65 = 78 failures (no allergies).

In the high outdoor activity group, we expect 180 x 0.41 = 73.8 successes (allergies) and 180 x 0.59 = 106.2 failures (no allergies).

All these counts are at least 10, which satisfies the condition for the sampling distribution to be approximately normal. Therefore, the correct choice is B.

Approximately normal, because we expect 42 successes and 78 failures from teenagers with low levels, and 73.8 and 106.2 from teenagers with high levels, and all of these counts are at least 10.

Answer 2

B

Step-by-step explanation: