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Is a 95% confidence interval twice as wide as a 47.5% confidence interval?

Is a 95% confidence interval twice as wide as a 47.5% confidence interval?

Breakingbank

A) twice as wide
B) more than twice as wide
C) less than twice as wide

And why?

Reply 1

Zacken

Original post by Breakingbank

A) twice as wide
B) more than twice as wide
C) less than twice as wide

And why?

95% has width:

2 \times 1.96 \times \frac{\sigma }{\sqrt{n}}

- what's the width of the 47.5% interval?

Reply 2

Gregorius

Original post by Breakingbank

A) twice as wide
B) more than twice as wide
C) less than twice as wide

And why?

Are you being asked this question as a school student or as a university student? If the former, then @Zacken has given you the appropriate method. If the latter, then the answer is "it's complicated" - and we'd need a bit more context to answer it.

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Is a 95% confidence interval twice as wide as a 47.5% confidence interval?

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