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(Solved): Assume that you are production manager of wheat production company. You selected 25 packages and fou ...


Assume that you are production manager of wheat production company. You selected 25 packages and found sample mean as 16.3 kg. You know that population variance is 0.16 .
A) Scenario 1: You wish that packages should be heavier than 16.1 kg on average. Test your claim and find p-value (significance is 5%).
B) Scenario 2 : Food regulation states that package weight should be 16 kg. Test validity of this regulation (significance level is 5%).
*Population variance is known -> use ‘’Z’’ distribution



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A) Hypotheses: Null hypothesis (H0): ? ? 16.1 (the average weight of the packages is less than or equal to 16.1 kg)
Alternative hypothesis (Ha): ? > 16.1 (the average weight of the packages is greater than 16.1 kg)

We will use a one-tailed Z-test because we are interested in testing the claim that the mean weight is greater than 16.1 kg.
Level of significance is 5%, which means ? = 0.05.

Since the population variance is known, we can use the Z-distribution.

Z-score can be calculated as:
  
where x? is the sample mean, ? is the population mean, ? is the population standard deviation (which is the square root of the population variance), and n is the sample size.
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