A 95% confidence interval for p, the proportion of all 12 grade students who dri

Question

A 95% confidence interval for p, the proportion of all 12 grade students who drive to school, was found to be (0.236, 0.282). Which of the following would be true about a 98% confidence interval constructed using the same data? The interval would be wider, because the critical value would be larger. The interval would be wider, because the standard error would be larger. The interval would be narrower, because the standard error would be smaller. The interval would be narrower, because the critical value would be smaller. The interval would be about the same width, because the standard error would be smaller, but the critical value would be larger.

Explanation / Answer

The confidence level % decides the critical value of z parameter that is used to compute the margin of error. Greater the confidence level %, greater is the critical value and hence greater is the width of the confidence interval.

Therefore the correct answer here is:

The interval would be wider, because the critical value would be larger.

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