Question

A machine set to fill soup cans with a mean of 20 ounces and a standard deviation of .11 oz. A random sample of 15 cans has a mean of 20.04 oz. Should the machine be reset?

Answer 1

solution

From the population, $\mu =20$ and $\sigma=0.11$

The sample mean, $\bar x =20.04$

$$z=\frac{\bar x - \mu}{\sigma}$$

$$z=\frac{20.04-20}{0.11}=0.3667$$

Since the machine could underfill or overfill the cans, we use a 2 tail distribution. At a 95% level of confidence, $z=1.96$ . Therefore we would reject the hypothesis that the two means are equal if the calculated $z\ value > 1.96$

answer:

At $z=0.3667,$ the samples filled are within the expected limits hence the machine should not be reset