Find the average rate of change for f(x)=x+6 over the interval [4,8]
2 answers:
<u>Answer: </u>
The Average rate of change for f(x) = x+6 over the interval (4,8) is 1
<u>Solution: </u>
We define the Average rate of function f(x) over the interval (a, b) as
--- eqn 1
From question, given that
f(x) =x+6 --- eqn 2
The interval is (4,8) .hence we say a = 4 and b = 8
The average rate of change for f(x) = x + 6 is given by using eqn 1
--- eqn 3
Where, by using eqn 2 , we get f(8) = 8+6 =14 and f(4) = 4+6 =10
Such that the required value would be f(8)-f(4) = 14-10 = 4
By substituting the values of f(8) and f(4) in eqn 3 ,the average rate of change for the given expression is
Hence the Average rate of change for f(x) = x+6 over the interval (4,8) is 1
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Answer:
We conclude that the mean family income for Mexican migrants to the United States is $27,000 per year and the provided information is consistent with the United Nations report.
Step-by-step explanation:
We are given that a United Nations report shows the mean family income for Mexican migrants to the United States is $27,000 per year.
A FLOC evaluation of 25 Mexican family units reveals a mean to be $30,000 with a sample standard deviation of $10,000.
Let = <em><u>true mean family income for Mexican migrants.</u></em>
So, Null Hypothesis, :
= $27,000 {means that the mean family income for Mexican migrants to the United States is $27,000 per year}
Alternate Hypothesis, :
$27,000 {means that the mean family income for Mexican migrants to the United States is different from $27,000 per year}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean family income = $30,000
s = sample standard deviation = $10,000
n = sample of Mexican family = 25
So, <u><em>the test statistics</em></u> = ~
= 1.50
The value of t test statistics is 1.50.
Since, in the question we are not given the level of significance so we assume it to be 5%. <u>Now, at 5% significance level the t table gives critical values of -2.064 and 2.064 at 24 degree of freedom for two-tailed test.</u>
Since our test statistic lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the mean family income for Mexican migrants to the United States is $27,000 per year and the provided information is consistent with the United Nations report.