According to the 2000 U.S. Census, 80% of Americans over the age of 25 have earned a high school diploma. Suppose we take a random sample of 120 Americans and record the proportion, p, of individuals in our sample that have a high school diploma.
Answers
Answer:
a) The mean is 0.8.
b) The standard deviation is 0.0365.
c) Normal
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
80% of Americans over the age of 25 have earned a high school diploma.
This means that [tex]p = 0.8[/tex]
Suppose we take a random sample of 120 Americans
This means that [tex]n = 120[/tex].
Question a:
The mean is:
[tex]\mu = p = 0.8[/tex]
The mean is 0.8.
Question b:
The standard deviation is:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.8*0.2}{120}} = 0.0365[/tex]
The standard deviation is 0.0365.
Question c:
By the Central Limit Theorem, approximately normal.
a) The mean is 0.8.
b) The standard deviation is 0.0365.
c) Normal
Here, we have,
we know that,
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean x and standard deviation σ, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean x and standard deviation s = σ/√n .
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean x=p and standard deviation s=√p(1-p)/n
80% of Americans over the age of 25 have earned a high school diploma.
This means that p=0.8
Suppose we take a random sample of 120 Americans
This means that n=120.
Question a:
The mean is:
x=p=0.8
The mean is 0.8.
Question b:
The standard deviation is:
s=0.0365
The standard deviation is 0.0365.
Question c:
By the Central Limit Theorem, approximately normal.
Learn more about standard deviation here:
brainly.com/question/23907081
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Step-by-step explanation:
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Of the population of all fruit flies we wish to give a 90% confidence interval for the fraction which possess a gene which gives immunity to fungal infections. To this end we have obtained a random sample of 400 fruit flies. We find that 280 of the flies in the sample possess the gene. Give the margin of error for the 90% confidence interval. Round your answer to 3 decimal places.
Answers
Answer:
The margin of error for the 90% confidence interval is of 0.038.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
To this end we have obtained a random sample of 400 fruit flies. We find that 280 of the flies in the sample possess the gene.
This means that [tex]n = 400, \pi = \frac{280}{400} = 0.7[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
Margin of error:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.645\sqrt{\frac{0.7*0.3}{400}}[/tex]
[tex]M = 0.038[/tex]
The margin of error for the 90% confidence interval is of 0.038.
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Step-by-step explanation:
https://answer-helper.com/mathematics/question16732528
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Answers
Answer:
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Step-by-step explanation:
First term:
7
7 ⋅ 4 = 28
Second term:
28
28 ⋅ 4 = 112
Third term:
112
112 ⋅ 4 = 448
Fourth term:
448
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aₙ = 7 ⋅ 4 ⁿ⁻¹
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Step-by-step explanation:
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Answers
Answer:
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Solution:
Given that,
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125 had traveled on an airplane
What is the ratio of total sixth-grade students to the number of students who had traveled on an airplane?
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Step-by-step explanation:
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