Can anyone answer this
2 answers:
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Answer:
So on this case the 95% confidence interval would be given by (5.56;6.96)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
The mean calculated for this case is
The sample deviation calculated
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Assuming a Confidence of 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (5.56;6.96)
Let's think about the information in the problem. The problem tells us a few key points:
- The number of rabbits grows exponentially
- We start with 20 rabbits (
,
)
- After 6 months (
), we have 100 rabbits (
)
Since we know we are going to be working with an exponential model, we can start with a base exponential model:
is the principal, or starting amount
is the growth/decay rate (in this case, growth)
is the number of months
is the number of rabbits
Based on the information in the problem, we can create two equations:
The first equation tells us that , or that we start with 20 rabbits. Thus, we can change the second equation to:
Now, we don't know , but we want to, so let's solve for it.
Now, the problem is asking us how many rabbits we are going to have after one year (), so let's find that:
After one year, we will have 500 rabbits.