Question

Students at Hope College were tested to see if they could determine the difference between tap water and bottled water. Of the 63 students tested, 42 correctly identified which was which. We will assume the students tested are representative of all students at Hope College. Using the 2SD rule, we find that the 95% confidence interval is (0.541, 0.793), and that the theory-based 95% confidence interval is (0.5503, 0.7831). Why are the 95% confidence intervals similar for the two methods?

Answer choices:

The intervals are similar because the validity conditions are not met.

The intervals are similar because the sample size is large.

Similar because validity conditions are met.

Answer 1

Solution :

When validity conditions are met, we get the 95% confidence interval using 2SD rule and theory-based 95% confidence interval similar.

Validity conditions :

np̂ > 10 and n(1 - p̂) ≥ 10.

We have, n = 63 and p̂ = 42/63

np̂ = 42 which is greater than 10.

n(1 - p̂) = 21 which is greater than 10.

Hence, validity conditions are met.

Hence, the 95% confidence intervals similar for the two methods because the validity conditions are met.

Third option is correct.