Question

The 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) Write the hypotheses for a two-tailed test of the claimed potassium content.
b) Assuming a known standard deviation of 2.00 mg. calculate the z test statistic to test the manufacturer's claim.
c) At the 1 percent level of significance (a = .01) does the sample exceed the manufacturer's claim?

Answer 1

Answer 2

The claim is that the mean potassium content in soft drink is not equal to 140mg.

a)

Test the null and alternative hypotheses,

Test the hypothesis at level of significance.

b)

For the sample of 20 bottles, the sample mean of potassium content obtained is 139.4mg.

The population standard deviation is 2.00mg.

The value of test statistic is calculated as follows:

The value of test statistic is

c)

The critical value of test statistic at is, . The decision rule is to reject null hypothesis if .

Since, the null hypothesis is failed to be rejected.

Thus, there is sufficient evidence to support the claim the mean potassium content in soft drinks is 140mg.

d)

The probability value of test statistic is calculated as follows:

Thus, the p-value of the test is 0.1797.