Suppose now that X is uniformly distributed on [h-3,h+3],\, for some unknown h. Using the Central Limit Theorem, identify the most appropriate expression for a 95\% confidence interval for h. You may want to refer to the normal table.
Normal Table
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\displaystyle \left[H-\frac{\sqrt{1.96 \cdot 3}}{\sqrt{n}},H+\frac{\sqrt{1.96 \cdot 3}}{\sqrt{n}}\right]
\displaystyle \left[H-\frac{1.96 }{\sqrt{3n}},H+\frac{1.96 }{\sqrt{3n}}\right]
\displaystyle \left[H-\frac{1.96\cdot \sqrt{3}}{\sqrt{n}},H+\frac{1.96\cdot \sqrt{3}}{\sqrt{n}}\right]
\displaystyle \left[H-\frac{1.96\cdot 3}{\sqrt{n}},H+\frac{1.96\cdot 3}{\sqrt{n}}\right]
incorrect
The most appropriate expression for a 95% confidence interval for h using the Central Limit Theorem is:
\displaystyle \left[H-\frac{1.96\cdot 3}{\sqrt{n}},H+\frac{1.96\cdot 3}{\sqrt{n}}\right]
The most appropriate expression for a 95% confidence interval for h, using the Central Limit Theorem, is:
\[ \left[H - \frac{1.96 \cdot 3}{\sqrt{n}}, H + \frac{1.96 \cdot 3}{\sqrt{n}}\right]\]
This expression takes into account the standard deviation of the distribution, which in this case is 3, and uses the z-score of 1.96 for a 95% confidence level.