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Halving the interval

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With $n = 25$ independent observations, a confidence interval for a mean has half-width $6$ . The standard deviation stays the same. How many observations in total are needed for the half-width to be $3$ ?

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Hint

The half-width is proportional to $\frac{1}{n}$ .

Solution

The half-width is proportional to $\frac{1}{n}$ .
Halving it requires $n$ to double.
So $n$ must be multiplied by $4$ .
The required total is $25 \times 4 = 100$ .
So the answer is $100$ .

Answer: $100$

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