Question

​Researchers conducted a follow-up study predicting the outcomes of races in the House of Representatives with 189 correct predictions out of 279. Using a simulation and the 2SD method, the 95% confidence interval is (0.62, 0.74) and using a theory-based approach, the 95% confidence interval for these data is (0.62, 0.73). When comparing the 2SD method and theory based confidence intervals, why are they similar?

Answer Choices:

-because the sample size is large

- because the validity conditions are met

-because the validity conditions are not met

Answer 1

For one proportion, the confidence interval formula while 2SD method is, Þ(1-ê) p+2x n By the theory method, the 95% confidence interval for one proportion is, p(1-P) p=20.05/2 n At 0.05 level of significance, from the normal area table values, the value of 20.05/2 is 1.96 (approximately 2). As the given sample size, 279, is sufficiently large, the value of margin of error value is almost equal in both the case. So, both the confidence intervals are same. So, the correct option is, “because the sample size is large”.