CUET · MATHS · PYQ PAPER 2025
Consider the following hypothesis \(H_0: \mu=315\) and \(H_a: \mu \neq 315\).
A sample of 60 provided a sample mean of 324.6 . The standard deviation ( \(\sigma\) ) is 14 and level of significance \(\alpha=0.05\). Then the confidence interval is :
[Given : \(Z_{\alpha / 2} \frac{14}{\sqrt{60}}=3.54\)]
- A \((321.06,328.14)\)
- B \((320.06,327.14)\)
- C \((322.06,327.14)\)
- D \((321.06,327.14)\)
Answer & Solution
Correct Answer
(A) \((321.06,328.14)\)
Step-by-step Solution
Detailed explanation
CI \( = \bar{x} \pm Z_{\alpha / 2} \frac{\sigma}{\sqrt{n}} \) CI \( = 324.6 \pm 3.54 \) Lower bound \( = 324.6 - 3.54 = 321.06 \) Upper bound \( = 324.6 + 3.54 = 328.14 \) CI \( = (321.06, 328.14) \)
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