If 95 % confidence interval for the population mean was reported to be 160 to 170 and =25, then size of the sample used in this study is: (Given Z_0.025=1.96 ) Option 1: 96 Option 2: 125 Option 3: 54 Option 4: 81

Answer: 96. Solution: For a confidence interval with known standard deviation: Half-width = z_(/2) * ()/√n Given: - Half-width = (170 - 160)/2 = 5 - z_0.025 = 1.96 - = 25 Plugging these values into the formula: 5 = 1.96 * 25/√n √n = (1.96 * 25)/5 √n = 49/5 n = (49/5)^2 = 2401/25 = 96.04 Therefore, the closest answer is 96.

Statistics & Applications

Inferential

Medium

applied

If $95 \%$ confidence interval for the population mean was reported to be $160$ to $170$ and $\sigma=25$ , then size of the sample used in this study is: (Given $\mathrm{Z}_{0.025}=1.96$ )

$96$

$125$

$54$

$81$

✅ Correct Option: 1

For a confidence interval with known standard deviation:

$\text{Half-width} = z_{\alpha/2} \cdot \dfrac{\sigma}{\sqrt{n}}$

Given:

Half-width $= (170 - 160)/2 = 5$ $= (170 - 160) /2 = 5$
- $z_{0.025} = 1.96$
- $\sigma = 25$

Plugging these values into the formula:

$5 = 1.96 \cdot \frac{25}{\sqrt{n}}$

$\sqrt{n} = \frac{1.96 \cdot 25}{5}$

$\sqrt{n} = \frac{49}{5}$

$n = \left(\frac{49}{5}\right)^2 = \frac{2401}{25} = 96.04$

Therefore, the closest answer is 96.

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If 95%95 \%95% confidence interval for the population mean was reported to be 160160160 to 170170170 and σ=25\sigma=25σ=25, then size of the sample used in this study is: (Given Z0.025=1.96\mathrm{Z}_{0.025}=1.96Z0.025​=1.96 )

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CUET Mathematics Past Year Questions (Topic-Wise)

If $95 \%$ confidence interval for the population mean was reported to be $160$ to $170$ and $\sigma=25$ , then size of the sample used in this study is: (Given $\mathrm{Z}_{0.025}=1.96$ )