Question

He mean potassium content of a popular sports drink is listed as 140 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sample mean of 139.4 mg. (a) State the hypotheses for a two-tailed test of the claimed potassium content.

(A) H0: μ = 140 mg vs. H1: μ ≠ 140 mg
(B) H0: μ ≤ 140 mg vs. H1: μ > 140 mg
(C) H0: μ ≥ 140 mg vs. H1: μ < 140 mg

Answer 1

Answer: (A) H0: μ = 140 mg vs. H1: μ ≠ 140 mg

Explanation:

Usually null hypothesis represents the claim that the values associated to the groups being tested have no statistical difference but alternative hypothesis supports the claim that there is statistical difference.

Let
`\mu` be the population mean .

We are given that the mean potassium content of a popular sports drink is listed as 140 mg in a 32-oz bottle.

i.e. Null hypothesis :
`H_0:\mu=140`

Alternative hypothesis for two tail hypothesis has sign (≠).

i.e. Alternative hypothesis :
`H_1 : \mu\\eq140`

∴ The hypotheses for a two-tailed test of the claimed potassium content:

H0: μ = 140 mg vs. H1: μ ≠ 140 mg