The sodium content of a popular sports drink is listed as 23

The sodium content of a popular sports drink is listed as 230 mg in a 32-oz bottle. Analysis of 13 bottles indicates a sample mean of 238.3 mg with a sample standard deviation of 20.9 mg.

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

(b) Calculate the t test statistic to test the manufacturer

Solution

(a) Let mu be the population mean

Ho: mu= 230 (i.e. null hypothesis)

Ha: mu not equal to 230 (i.e. alternative hypothesis)

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(b) The test statisitc is

t=(xbar-mu)/(s/vn)

=(238.3-230)/(20.9/sqrt(13))

=1.43187

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(c) The degree of freedom =n-1=13-1=12

It is a two-tailed test.

Given a=0.02, the critical values are t(0.01, df=12) =-2.68 or 2.68 (from student t table)

The rejection regions are if t<-2.68 or t>2.68, we reject the null hypothesis.

Since t=1.43187 is between -2.68 and 2.68, we do not reject the null hypothesis.

So we can not conclude that the sample contradict the manufacturer