Question

one hundred pieces of a certain yarn were tested for strength, the mean value of the test results being 60N and their standard deviation 3N. calculate 95% confidence limits for the true mean strength of the yarn. if it was required to estimate the true mean correct to 1/2N . how many tests should be testes should be performed?

Answer 1

Given, mean $\mu=60N,\sigma=3N$

$\alpha=0.05$

$\dfrac{\alpha}{2}=0.025, Z_{\frac{\alpha}{2}}=z_{0.025}=1.96$

95% confidence limit for true mean strength is given by-

$= \mu\pm Z_{\frac{\alpha}{2}}\dfrac{\sigma}{\sqrt{n}} \\ =60\pm 1.96\times \dfrac{3}{\sqrt{100}} \\ =60\pm 0.588 \\ =(59.412,60.588)$

If we required to estimate the true mean correct to $\dfrac{1}{2}N$ , Then The number of test we would have to perform is two, The first is the t-test for independent sample and second test is p-value test.