Question

w pay OLUU for the upgrade. 6(15%) A researcher worker wants to determine the average time it takes a mechanic to rotate the tires of a car and she wants to be able to assert with a 95% confidence that the mean of her sample is off by at most 0.50 minutes. It is known that o = 1.6 minutes and the time of rotation is normally distributed. How large a sample size will she have to take? Frequently used z values: 205 = 1.645, 20.025 = 1.96, 20.005 = 2.576.

Answer 1

Solution:

We are given:

$\sigma=1.6,E=0.50,C-level=95\%$

The sample size required is:

$n=\left ( \frac{z_{\frac{0.05}{2}}\times \sigma}{E} \right )^{2}$

  $=\left ( \frac{1.96\times 1.6}{0.50} \right )^{2}$

  $=39.337984\approx 39$

Therefore, the sample size required is 39