The formula for compounded interest in this type of equation is:
where A is the amount at the end of the time period, P is the principal amount you start with, R is the interest rate, N is the amount of compound periods, and T is the time allotted for the money to gain interest.
P = 5000, R = 3% or 0.03, N = monthly so 12, T = 2 years
Plug in our given information into the equation:
Let the calculator do the work here...
A ≈ 5308.785 which rounds to A ≈ 5308.79
Option A is your answer.
Answer:
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense
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
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
We need to conduct a hypothesis in order to check if the true mean is 0.5 or no, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense
<u>Answer:</u>
Annual Income of A=
and
Annual Income of B=
<u>Step-by-step explanation:</u>
<u>Given Data:</u>
Ratio of annual income of A and B=4:3
Ratio of expenditures of A and B=3:2
Saving of A and B=1000
<u>Required:</u> Annual Income of A and B=?
<u>Solution:</u>
If ratio of income of A and B is 4:3
then let Income of A= and Income of B=
If ratio of expenditure of A and B is 3:2
then let expenditure of A= and expenditure of B=
Therefore,
...........
and ..........
subtracting Eq(1) and Eq(2), we get
putting in Eq(1), we get value of
as
because x and y are equal in Eq (3)
Now, Annual Income of A=
and Annual Income of B=