Question

In: Statistics and Probability

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

  1. (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?

  1. (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 2 years ago
Next > < Previous

Related Solutions

The Food and Drug Administration (FDA) is asked to approve a new drug. The new drug...
The Food and Drug Administration (FDA) is asked to approve a new drug. The new drug should contain less than 25mg of the active ingredient “toxin”, which is assumed to have dangerous side effects. The FDA would like to restrict the error of “approving the drug despite its too high content of toxin” to a maximum risk of 5% (α ≤ 0.05). Let Xi : “ The content of toxin in the i-th pill [in mg].” ∼ N(µ, σ2 )...
A drug company applied for the approval of the Food and Drug Administration (FDA) to market...
A drug company applied for the approval of the Food and Drug Administration (FDA) to market a miracle drug that the company believed could cure some cancers. During the period that the application was under consideration the company's stock rose to $65 per share. The president of the company learned that the FDA application was about to be denied. You are a personal friend of the president, and he told you that he believed that the stock will start trading...
The Food and Drug Administration (FDA) is an agency of the United States Department of Health...
The Food and Drug Administration (FDA) is an agency of the United States Department of Health and Human Services, one of the United States' federal executive departments. The FDA is responsible for protecting and promoting public health through the regulation and supervision of food safety, tobacco products, prescriptions, and other health-related products. The following are a few examples of the powers the FDA has: • Most federal laws concerning the FDA are part of the Food, Drug, and Cosmetic Act....
The U.S. Food and Drug Administration (FDA) requires nutrition labeling for most foods. Under FDA regulations,...
The U.S. Food and Drug Administration (FDA) requires nutrition labeling for most foods. Under FDA regulations, manufacturers are required to list the amounts of certain nutrients in their foods, such as calories, sugar, fat, and carbohydrates. This nutritional information is displayed on the food’s package. Calories (C) Sugar (S) Fat (F) Carbohydrates (R) 100 12 0.5 25 130 11 1.5 29 100 1 2 20 130 15 2 31 130 13 1.5 29 120 3 0.5 26 100 2 0...
Many consumer groups feel that the U.S. Food and Drug Administration (FDA) drug approval process is...
Many consumer groups feel that the U.S. Food and Drug Administration (FDA) drug approval process is too easy and, as a result, too many drugs are approved that are later found to be pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. Consider a null hypothesis that a new, unapproved drug is unsafe and an alternative hypothesis that a new, unapproved drug is safe. Differentiate Type 1 and Type...
1. The The Food and Drug Administration (FDA) requires which ONE of the following products to...
1. The The Food and Drug Administration (FDA) requires which ONE of the following products to contain specific levels of microbial inhibitors or acidifying agents such as phosphoric or citric acid to prevent production of Clostridium botulinum toxin in the product? (NOTE: An anaerobic environment is present in both bottled and canned products. ) Hint: Look at the lecture slides that discuss how some of these products are made. You can also look up specific information for these items on...
1. The The Food and Drug Administration (FDA) requires which ONE of the following products to...
1. The The Food and Drug Administration (FDA) requires which ONE of the following products to contain specific levels of microbial inhibitors or acidifying agents such as phosphoric or citric acid to prevent production of Clostridium botulinum toxin in the product? (NOTE: An anaerobic environment is present in both bottled and canned products. ) Hint: Look at the lecture slides that discuss how some of these products are made. You can also look up specific information for these items on...
It was recently announced that the Food and Drug Administration (FDA) will extend its regulatory authority...
It was recently announced that the Food and Drug Administration (FDA) will extend its regulatory authority to E-cigarettes, tobacco pipes, and cigars. They have proposed a ban of these products to those under 18 (in person and Internet sales), those purchasing these products must show identification, a ban on use in public places, and products must include warning labels. The producers of cigars and e-cigarettes must register with the FDA, provide a detailed accounting of their product ingredients, disclose their...
The U.S. Food and Drug Administration (FDA) recently approved the marketing of a new chemical solution,...
The U.S. Food and Drug Administration (FDA) recently approved the marketing of a new chemical solution, Caridex, which disolves cavities. In a study conducted by dental researchers at Northwestern University, 21 of the 35 patients with cavities preffered treatment with Caridex to drilling (Gainesville Sun, Feb. 11, 1988). Find a 90% confidence interval for the true proportion of dental patients who prefer having cavities dissolved with Caridex rather than drilled. (0.46,0.74) (0.44,0.76) (0.39,0.81)
1. In 1995, the Food and Drug Administration (FDA) published new labeling standards for bottled water....
1. In 1995, the Food and Drug Administration (FDA) published new labeling standards for bottled water. (The full text of the final rule can be found at http://cfr.vlex.com/vid/165-110-bottled-water-19705533.) Prior to that time, bottlers could sell regular tap water under a bottled water label. In fact, the FDA estimated that approximately 25 percent of the supply of bottled water was nothing more than ordinary tap water. (a) Consider how these tougher standards eliminated 25 percent of the supply of bottled water....
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT