A 95 confidence interval for p the proportion of all 12 grade students

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? Please show work if applicable and provide explanation for the answer.

A) The interval would be wider, because the critical value would be larger.
B) The interval would be narrower, because the critical value would be smaller.
C) The interval would be wider, because the standard error would be larger.
D) The interval would be about the same width, because the standard error would be smaller, but the critical value would be larger.
E) The interval would be narrower, because the standard error would be smaller.

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