SOLUTION: A consumer protection group randomly checks the volume of different beverages to ensure that companies are packaging the stated amount. Each individual volume is not exact, but a v

Question 1071969: A consumer protection group randomly checks the volume of different beverages to ensure that companies are packaging the stated amount. Each individual volume is not exact, but a volume of iced tea beverages is supposed to average to 300 mL with a standard deviation of 3 mL. The consumer protection group sampled 20 beverages and found the average to be 298.4 mL. Which of the following is the most restrictive level of significance on a hypothesis test that would indicate the company is packaging less than the required average 300 mL?
1%
2.5%
5%.
10%
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe 1% would do it.
that would give you a critical z-factor of plus or minus 2.327.

the z-factor of your sample would be calculated as follows:

sample size = 20
mean = 298.4
population standard deviation = 3

standard error = standard deviation of the population / square root of the sample size.

that would be equal to 3/sqrt(20).

z-score = (sample mean minus standard mean) / (3/sqrt(20).

that would be equal to (298.4 - 300) / (3/sqrt(20) which would be equal to -2.385.

the z-score calculator i used can be found at:

http://davidmlane.com/hyperstat/z_table.html

the first picture is calculating the critical z-score from an alpha of .01 on the low side of the distribution curve.

this means that less than 1% of the z-scores will be below this critical z-score.

the second picture is calculating the alpha for the z-score of the sample.

the samle z-score is below the critical z-score at an alpha of 1% which indicates the results of the test are statistically significant.

the alpha of the sample is less than the alpha of the critical z-score which tells you the same thing.

the sample would have failed all of the alphas shown, but 1% is the most restrictive alpha that it would have failed.

$$$

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