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 2 years agoRelated 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
ADVERTISEMENT
Latest Questions
- Write a C++ program that reads integers from standard input until end of file. Print out...
- Woo Audio is a small company in New York that makes high-quality headphone amplifiers. The company...
- How are users categorized? In Linux, which user has all the privileges? Why do we need...
- Force Table: If the center ring were to have considerable mass, what effect would it have...
- 1. Mark Welsch deposits $7,100 in an account that earns interest at an annual rate of...
- Can someone please explain to me what are the differences between Windows and Linux memory hierarchy,...
- Research a company that has had some consolidation with a foreign subsidiary and discuss whether that...
ADVERTISEMENT