Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 447.0 gram setting. It is believed that the machine is underfilling the bags. A 41 bag sample had a mean of 443.0 grams. A level of significance of 0.02 will be used. Determine the decision rule. Assume the standard deviation is known to be 21.0.

Answer 1

Answer:

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 447.0 gram setting.

So, Null hypothesis : $H_0:\mu =447$

It is believed that the machine is under filling the bags

So, Alternate hypothesis : $H_a:\mu<447$

n = 41

Population standard deviation = $\sigma = 21$

x = 443

We will use z test since n > 30 and we are given the population standard deviation.

Formula : $z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$z=\frac{443-447}{\frac{21}{\sqrt{41}}}$

$z=-1.2196$

Use z table to find p value

p value = 0.1131

α = 0.02

p value > α

So, we fail to reject null hypothesis.

So, its bag filling machine works correctly at the 447.0 gram setting.