Question

Soda Tak claims that Diet Tak has 40mg of sodium per can. You work for a consumer organization that tests such claims. You take a random sample of 60 cans and find that the mean amount of sodium in the sample is 41.9mg. The population standard deviation in all cans is 5.2mg. You suspect that there is more than 40mg of sodium per can. Find the z-score.

Answer 1

Z - score = 2.83

Explanation:

Given the following :

Number of samples (N) = 60

Sample mean (x) = 41.9mg

Population mean (μ) = 40mg

Population standard deviation (sd) = 5.2

Using the relation :

Z = (x - μ) / (sd / √N)

Z = (41.9 - 40) / (5.2 / √60)

Z = 1.9 / (5.2 / 7.7459666)

Z = 1.9 / 0.6713171

Z = 2.8302570

Therefore, the z-score = 2.83