Question

The mean potassium content of a popular sports drink is listed as 139 mg in a 32-oz bottle. Analysis of 24 bottles indicates a sample mean of 137.5 mg.

(a)	State the hypotheses for a two-tailed test of the claimed potassium content.

a.	H0: μ = 139 mg vs. H1: μ ≠ 139 mg
b.	H0: μ ≤ 139 mg vs. H1: μ > 139 mg
c.	H0: μ ≥ 139 mg vs. H1: μ < 139 mg

	a b c

(b)	Assuming a known standard deviation of 2.3 mg, calculate the z test statistic to test the manufacturer’s claim. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.)

Test statistic

(c)	At the 1 percent level of significance (α = 0.01) does the sample contradict the manufacturer’s claim?
	Decision Rule: Reject H0   (Click to select)  if z > + 2.576 or if z < -2.576  if z < + 2.576 or if z < -2.576  if z < + 2.576 or if z > -2.576
	The sample  (Click to select)  contradicts  does not contradict  the manufacturer's claim.

(d)	Find the p-value. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal places.)

p-value

Answer 1

a. Here we need to state the hypotheses for a two-tailed test of the claimed potassium content, which mean

Hence answer here is a.

H0: μ = 139 mg vs. H1: μ ≠ 139 mg

b. Now and

So test statistics is

c. The z-critical values for a two-tailed test, for a significance level of α=0.01

zc​=−2.576 and zc​=2.576

Graphically

Decision Rule: Reject H0 if z > + 2.576 or if z < -2.576

As test statistics falls in the rejection region we reject the null hypothesis

d. P value is