The admissions director for a university found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen. Is the following explanation correct, based on that information? There is a 95% probability that the interval from 107.8 to 116.2 contains ?¯x¯. Incorrect. The point estimate ?¯x¯ will always be in the center of the confidence interval, so there is a 100% chance that ?¯x¯ will be in the interval. Incorrect. If we take many samples, about 95% of them will contain the interval (107.8, 116.2) Incorrect. It should say that there is a 95% probability that the interval from 107.8 to 116.2 contains ?μ. Incorrect. 95% of the students at this university have an IQ between 107.8 and 116.2. Correct. That is the meaning of 95% confidence.

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.