According to the United States Census Bureau (2011 data), there are approximately 55,500,000 married couple households in the Un
ited State. Every married-couple household is classified into one of three categories:
• both native which means that both spouses were born in the U.S.
• both foreign which means that both spouses were born outside of the U.S.
• one native, one foreign which means that one spouse was born in the U.S. and one was born outside of the U.S..
If 79.5% of married couple households are both native and 13.2% are both foreign, then
(a) what percentage of married couple households are one native, one foreign
7.3
Correct: Your answer is correct.
% married couple households are one native, one foreign
(b) how many married couple households are one native, one foreign?
Incorrect: Your answer is incorrect.
married couple households are one native, one foreign
• both native which means that both spouses were born in the U.S.
• both foreign which means that both spouses were born outside of the U.S.
• one native, one foreign which means that one spouse was born in the U.S. and one was born outside of the U.S..
If 79.5% of married couple households are both native and 13.2% are both foreign, then
(a) what percentage of married couple households are one native, one foreign
7.3
Correct: Your answer is correct.
% married couple households are one native, one foreign
(b) how many married couple households are one native, one foreign?
Incorrect: Your answer is incorrect.
married couple households are one native, one foreign
1 answer:
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Answer:
(I) 99% confidence interval for the mean nicotine content of this brand of cigarette is [24.169 mg , 30.431 mg].
(II) No, since the value 28.4 does not fall in the 98% confidence interval.
Step-by-step explanation:
We are given that a new cigarette has recently been marketed.
The FDA tests on this cigarette gave a mean nicotine content of 27.3 milligrams and standard deviation of 2.8 milligrams for a sample of 9 cigarettes.
Firstly, the Pivotal quantity for 99% confidence interval for the population mean is given by;
P.Q. = ~
where, = sample mean nicotine content = 27.3 milligrams
s = sample standard deviation = 2.8 milligrams
n = sample of cigarettes = 9
= true mean nicotine content
<em>Here for constructing 99% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>
<u>Part I</u> : So, 99% confidence interval for the population mean, is ;
P(-3.355 < < 3.355) = 0.99 {As the critical value of t at 8 degree
of freedom are -3.355 & 3.355 with P = 0.5%}
P(-3.355 < < 3.355) = 0.99
P( <
<
) = 0.99
P( <
<
) = 0.99
<u />
<u>99% confidence interval for</u> = [
,
]
= [ ,
]
= [27.3 3.131]
= [24.169 mg , 30.431 mg]
Therefore, 99% confidence interval for the mean nicotine content of this brand of cigarette is [24.169 mg , 30.431 mg].
<u>Part II</u> : We are given that the FDA tests on this cigarette gave a mean nicotine content of 24.9 milligrams and standard deviation of 2.6 milligrams for a sample of n = 9 cigarettes.
The FDA claims that the mean nicotine content exceeds 28.4 milligrams for this brand of cigarette, and their stated reliability is 98%.
The Pivotal quantity for 98% confidence interval for the population mean is given by;
P.Q. = ~
where, = sample mean nicotine content = 24.9 milligrams
s = sample standard deviation = 2.6 milligrams
n = sample of cigarettes = 9
= true mean nicotine content
<em>Here for constructing 98% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>
So, 98% confidence interval for the population mean, is ;
P(-2.896 < < 2.896) = 0.98 {As the critical value of t at 8 degree
of freedom are -2.896 & 2.896 with P = 1%}
P(-2.896 < < 2.896) = 0.98
P( <
<
) = 0.98
P( <
<
) = 0.98
<u />
<u>98% confidence interval for</u> = [
,
]
= [ ,
]
= [22.4 mg , 27.4 mg]
Therefore, 98% confidence interval for the mean nicotine content of this brand of cigarette is [22.4 mg , 27.4 mg].
No, we don't agree on the claim of FDA that the mean nicotine content exceeds 28.4 milligrams for this brand of cigarette because as we can see in the above confidence interval that the value 28.4 does not fall in the 98% confidence interval.