Question

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 1

the correct answer is 2.5%

Answer 2

2.5%

Explanation:

Sample size n = 20

Sample mean x bar = 298.4

Sigma = population std deviaton = 3

mu = population mean = 300 mL

t statistic = x bar-mu/Std error

STd error = std deviation/sqrt of n

= 3/4.47=0.6711

Hence t statistic = (298.4-300)/0.6711

=-2.38

df =20-1 =19

p value for this is 0.013=1.3%

Note that p vaue >1% but less than 2.5%, 5% and 10%

Hence the restrictive value most is 2.5%