Which is greater 6/12 or 1/3
1 answer:
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Answer:
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Step-by-step explanation:
Answer:
a) 0.24356 or 24.36%
b) [102.39 , 105.61]
c) The interpretation of this confidence interval is that in samples of 427 people aged 65 years and older, there is a 99% probability that the number of people that suffers sleep apnea is between 103 and 105.
Step-by-step explanation:
a)
This can be considered a binomial distribution (a person either has sleep apnea or not).
Based on the sample we have the probability of suffering the condition is
p = 104/427 = 0.24356
and q (the probability of not suffering the condition) is
q=1-0.24356=0.75644
So the proportion of people aged 65 years and older who have sleep apnea is 0.24356 or 24.36%
b)
To check if we can <em>approximate this binomial distribution with the Normal distribution</em> we must see that
np ≥ 5 and nq ≥ 5
where n is the sample size. Since
427*0.24356 ≥ 5 and 427*0.75644 ≥ 5
we can approximate the binomial with a Normal distribution with mean
np = 427*0.24356 = 104
and standard deviation
The 99% confidence interval (without the continuity correction factor) is given by the interval
where
<em>is the sample mean </em>
<em>s is the sample standard deviation </em>
<em>n is the sample size </em>
<em>is the 0.01 (99%) upper critical value for
</em>
<em>the Normal distribution N(0;1). </em>
The value of can be found either by using a table or a computer to find it equals to
and our 99% confidence interval <em>(without continuity correction) </em>is
We can now introduce the continuity correction factor. This should be done because <em>we are approximating a discrete distribution (Binomial) with a continuous one (Normal). </em>
This is simply done by widening the interval in 0.5 at each end, so our final 99% confidence interval is
[102.3946 , 105.6054] = [102.39 , 105.61] rounded to 2 decimal places.
c)
The interpretation of this confidence interval is that in samples of 427 people aged 65 years and older, there is a 99% probability that the number of people that suffers sleep apnea is between 103 and 105.
If another study found a 15% of elderly people suffered sleep apnea, that would mean that in a sample of 427 only 64 would have the condition. Since that number is less than 103 by far, that would give us a reason to doubt about the conditions that framed the study (sample size, sampling method, age of people, etc.)
Answer:
The question is re-framed:
During a recent rainstorm,8 centimeters of rain fell in Dubaku's hometown, and 2 point,36 centimeters of rain fell in Elliot's hometown. During the same storm, 15 point, 19 centimeters of snow fell in Alperen's hometown. How much more rain fell in Dubaku's town than in Elliot's town? In centimeters.
Rain fall on Dubaku's town is more than of Elliots's town.
Step-by-step explanation:
Rainfall on Dubaku's hometown on the day of the rain storm
Rainfall on Elliots's hometown on the day of the rain storm
How much more rain fell in Dubaku's town = Difference of the rainfall on Dubaku's and Elliots's hometown.
So the difference .
Our final answer centimeters.