Question

In: Statistics and Probability

(20pts) The Food and Drug Administration (FDA) has established an upper tolerance of 5 parts per...

(20pts) The Food and Drug Administration (FDA) has established an upper tolerance of 5 parts per billion for the cancer-causing substance nitrosamine in beer. Suppose that Pabst and Miller are identified by the FDA as containing excessive concentrations of nitrosamines and are tested by an independent testing agency with the results shown in the accompanying table (in parts per billion). Also suppose that 36 bottles were randomly selected from each brand.

                     Stat.     Pabst    Miller
                     --------  -----    ------
                     Mean      5.25     5.31
                     Std. Dev. 1.20     1.44

Specify the null and alternative hypotheses. What are the test statistics for these tests?

(20pts) What is the p-value(s) for question (3)? Do the results of the independent testing agency provide sufficient evidence to conclude that either brand of beer contains a mean nitrosamine concentration in excess of the FDA standard? Use a level of significance of .05.

Solutions

Expert Solution

t test for Single population

For Pabst

Given: = 5, = 5.25, s = 1.2, n = 36, = 0.05

The Hypothesis:

H0: = 5

Ha: > 5

This is a right tailed Test.

The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

The p Value: The p value (Right Tail) for t = 1.25, for degrees of freedom (df) = n-1 = 35, is; p value = 0.1098

The Decision Rule: If P value is < , Then Reject H0.

The Decision: Since P value (0.1098) is > (0.05) , We Fail to Reject H0.

The Conclusion: There isn't sufficient evidence at the 95% significance level to conclude that Abst contains a mean nitrosamine concentration in excess of the FDA standard.

__________________________________________________________

For Miller

Given: = 5, = 5.31, s = 1.44, n = 36, = 0.05

The Hypothesis:

H0: = 5

Ha: > 5

This is a right tailed Test.

The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

The p Value: The p value (Right Tail) for t = 1.29, for degrees of freedom (df) = n-1 = 35, is; p value = 0.1028

The Decision Rule: If P value is < , Then Reject H0.

The Decision: Since P value (0.1028) is > (0.05) , We Reject -- Fail to Reject H0.

The Conclusion: There isn't sufficient evidence at the 95% significance level to conclude that Miller contains a mean nitrosamine concentration in excess of the FDA standard.

_______________________________________

No, the testing agency does not have sufficient evidence to conclude that either brand contains a mean nitrosamine concentration in excess of the FDA standard.

_______________________________________

orchestra answered 1 year ago

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