CUET · MATHS · PYQ PAPER 2025
A machine has been producing steel tubes of mean inner diameter of 2 cm.
A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm.
Test the hypothesis that the machine is working in the proper order at 5% level of significance and answer, which of the following statements are correct?
[Given that \(t_{0.05}=2.262\)]
(A) The value of the test statistic is t = 0.476
(B) The null hypothesis is rejected at \(5 \%\) level of significance.
(C) The null hypothesis is accepted at \(5 \%\) level of significance.
(D) The degree of freedom is 10
Choose the correct answer from the options given below:
- A (A), (B) and (D) only
- B (A), (C) and (D) only
- C (A) and (C) only
- D (C) and (D) only
Answer & Solution
Correct Answer
(C) (A) and (C) only
Step-by-step Solution
Detailed explanation
\(df = n - 1\) \(df = 10 - 1 = 9\) \(t = \frac{\bar{x} - \mu}{s / \sqrt{n-1}}\) \(t = \frac{2.01 - 2}{0.063 / \sqrt{10-1}}\) \(t = \frac{0.01}{0.063 / 3}\) \(t = \frac{0.01}{0.021} \approx 0.476\) Given \(t_{0.05} = 2.262\). \(|t_{calculated}| = 0.476\) Since…
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