Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 418 gram setting. It is believed that the machine is underfilling the bags. A 9 bag sample had a mean of 411 grams with a standard deviation of 20 . A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

Answer 1

Answer: There is sufficient evidence to support the claim that the bags are under-filled.

Explanation:

Since we have given that

`H_0:\mu=418\\\\H_a:\mu<418`

Sample mean = 411

Standard deviation = 20

n = 9

So, the test statistic value is given by

`z=\frac{\bar{x}-\mu}{(\sigma)/(√(n))}\\\\\\z=(411-418)/((20)/(√(9)))\\\\\\z=(-7)/((20)/(3))\\\\\\z=-1.05`

At 0.025 level of significance,

critical value z = -2.306

since -2.306<-1.05

so, we will reject the null hypothesis.

Yes, there is sufficient evidence to support the claim that the bags are underfilled.