Question

If the standard deviation of shear strength measurements for spot welds is 9.5 pounds per square inch (psi), what is the minimum number of test welds that should be sampled if we want the sample mean to be within 1.4 psi of the true mean with probability approximately 0.99

Answer 1

Answer: 306

Step-by-step explanation:

Formula to find sample size:

$n=(\dfrac{\sigma\times z^*}{E})^2$ , where $\sigma$ = standard deviation, E = margin of error, z* = critrical z-value.

As per given,

$\sigma=9.5 , E=1.4$

Critical z-value for 99% confidence = 2.576

Now , the minimum sampl size :$n=(\dfrac{9.5\times2.576}{1.4})^2$

$\Rightarrow\ n=305.5504\approx306$

Hence, the required sample size = 306