Question

ecn 221 The sodium content of a popular sports drink is listed as 206 mg in a 32-oz bottle. Analysis of 14 bottles indicates a sample mean of 217.5 mg with a sample standard deviation of 14.9 mg. (a) State the hypotheses for a two-tailed test of the claimed sodium content.

Answer 1

`H_(0): \mu = 206\text{ mg}\\H_A: \mu \\eq 206\text{ mg}`

Explanation:

We are given the following in the question:

Population mean, μ = 206 mg

Sample mean,
`\bar{x}` = 217.5 mg

Sample size, n = 14

Sample standard deviation, s = 14.9 mg

Claim:

The mean sodium content for the sports drink is not 206 mg. It is different than 206 mg.

Thus, we design the null and the alternate hypothesis

`H_(0): \mu = 206\text{ mg}\\H_A: \mu \\eq 206\text{ mg}`

We use two-tailed t test to perform this hypothesis.