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%

Question

Abby Murray

Mathematics

27 June, 20:15

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%

+2

Answers (1)

Know the Answer?

Damian Wilcox · Answer 1

The most restrictive level of significance on a hypothesis test that would indicate the company is packaging less than the required average 300 mL is 1%.

The solution would be like this for this specific problem:

sample size = 20

mean = 298.4

population standard deviation = 3

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

= 3/sqrt (20

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

= (298.4 - 300) / (3/sqrt (20)

= - 2.385

Probability below - 2.385 with above 1.96, between - 1.96 and 1.96, and outside - 1.96 and 1.96 is 1%.