The sodium content of a popular sports drink is listed as 21

The sodium content of a popular sports drink is listed as 212 mg in a 32-oz bottle. Analysis of 17 bottles indicates a sample mean of 227 mg with a sample standard deviation of 18.8 mg.

13.

State the hypotheses for a two-tailed test of the claimed sodium content.

Solution

sample size,n = 17
sample mean,xbar = 227
standard deviation,s = 18.8

a.
H0: u = 212
H1: u is not equal to 212

b.
test statistic, t = (xbar-u)/(s/sqrt(n))
t = (227-212) / (18.8/sqrt(17))
t = 3.2900

c.
alpha,a = 0.01
critical value = +/- t(a/2,n-1) = +/- t(0.005, 16)
critical value = +/- 2.921

non-critical region is interval: (-2.921 , 2.921)
since t lies outside the interval, hence reject H0
Reject H0. The sample contradict the manufacturer\'s claim.

d.
1.
degree of freedom = n-1 = 16
Since it is a 2-tailed test hence
P_value = 0.0046

2.
Since P_value < 0.01(=alpha) hence reject H0
Yes we come to the same conclusion.