Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404 gram setting. It is believed that the machine is underfilling the bags. A 27 bag sample had a mean of 402 grams with a variance of 676. A level of significance of 0.1 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

There is no sufficient evidence to support the claim that the bags are underfilled

Explanation:

We are given;

n = 27 bags

Sample mean;X = 402 gram

Population mean;μ = 404 gram

Variance = 676

We know that, standard deviation(σ) = √variance

Thus;

σ = √676

σ = 26

The hypotheses are;

Null hypothesis; H0: μ = 404

Alternative hypothesis; HA: μ < 404

Let's find the z-score from the formula;

z = (X - μ)/(√σ/n)

z = (402 - 404)/√(26/27)

z = -2.04

From the z-distribution table attached, we have a p-value of 0.02068

This is less than the significance value of 0.01 and thus we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that the bags are underfilled