A company 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 variance of 0.0004 cm2. The value of test statistic is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.5
Given:
Population mean: $\mu = 2$ cm
Sample size: $n = 10$
Sample mean: $\bar{x} = 2.01$ cm
Sample variance: $s^2 = 0.0004 \Rightarrow s = \sqrt{0.0004} = 0.02$ cm
Test statistic (t-test for mean, small sample, unknown population variance):
$t = \frac{\bar{x} - \mu}{s / \sqrt{n}} = \frac{2.01 - 2}{0.02 / \sqrt{10}} = \frac{0.01}{0.0063246} \approx 1.50$