Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 426 gram setting. Based on a 13 bag sample where the mean is 433 grams and the standard deviation is 29, is there sufficient evidence at the 0.05 level that the bags are overfilled? Assume the population distribution is approximately normal.

Answer 1

The conclusion of the research is that we reject the null hypothesis and we conclude that the bag filling machine does not work correctly at the 426 gram setting.

How to solve hypothesis testing?

We are given;

Population Mean; μ = 426

Sample mean; x' = 433

Sample size; n = 13

Standard deviation; s = 29

significance level; α = 0.05

Let us define the hypotheses;

Null Hypothesis; H₀: μ = 426 g

Alternative Hypothesis; H_a: μ < 426 g

Formula for the z-score here is;

z = (x' - μ)/(s/√n)

z = (433 - 426)/(29/√13)

z = 0.87

From online p-value from z-score calculator, we have;

p-value =  0.1922

This p-value is greater than the significance value and as such we reject the null hypothesis and we conclude that the bag filling machine does not work correctly at the 426 gram setting.

Read more about Hypothesis testing at; brainly.com/question/15980493

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