Question

In-line skaters A study of injuries to in-line skaters used data from the National Electronic Injury Surveillance System, which collects data from a random sample of hospital emergency rooms. The researchers interviewed 161 people who came to emergency rooms with injuries from in-line skating. Wrist injuries (mostly fractures) were the most common.
The interviews found that 53 people were wearing wrist guards and 6 of these had wrist injuries. Of the 108 who did not wear wrist guards, 45 had wrist injuries. Why should we not use the large-sample confidence interval for these data?

a. Because 161 people are not enough for using the large-sample confidence interval.
b. Because the difference in sizes of the two groups is too large.
c. Because there are only 6 skaters in one group having wrist injuries.
d. Because the sample error is two large.

Answer 1

Using the Central Limit Theorem, it is found the correct option regarding why the large-sample confidence interval for these data.

c. Because there are only 6 skaters in one group having wrist injuries.

What does the Central Limit Theorem state?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$, as long as $np \geq 10$ and $n(1 - p) \geq 10$, that is, as long as there are at least 10 successes and at least 10 failures in the sample.

In this problem, for the sample of people wearing wrist guards, only 6 had injuries, hence the large-sample confidence interval should not be used and option C is correct.

To learn more about the Central Limit Theorem, you can check brainly.com/question/24663213