25 Points!!! Need to be Done Now Please. Priority
1 answer:
9514 1404 393
Answer:
- x2 = .72413793
- x3 = .087249546
Step-by-step explanation:
Modern graphing calculators have a derivative function available, so using a calculator to find the next value of x is pretty simple.
The Newton's Method iterator for finding the next approximation to the root (x') is ...
x' = x -f(x)/f'(x) . . . . . where f'(x) is the derivative of f(x).
The attachment shows the first 3 iterations (4 approximations). We observe that the starting point is pretty far from the root, and on the wrong side of some wiggles in the function, so convergence is pretty slow.
The desired approximations are shown above and in the table below.
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<em>Additional comment</em>
To 12 significant figures, the only real root is −1.10305899649. When the calculator can interactively produce a next guess, you can type the next guess value into the iterator function even as it is showing you the next value. This lets you find the best-precision result as fast as you can type it.
For a calculator like a TI-84, the iterator function can make repeated use of "Ans" as an argument. It usually doesn't take more than 3 or 4 iterations to get a best-precision result, since the number of good decimal places is about doubled on each iteration. (Of course, you have to start with a better approximation than the one given in this problem.)
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Answer:
If we compare the p value and the significance level given for example we see that
so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.
Step-by-step explanation:
1) Data given and notation
represent the sample mean
represent the standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the mean score is higher than 48, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't know the population deviation, so for this case 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:
Calculate the P-value
First we find the degrees of freedom:
Since is a one-side upper test the p value would be:
Conclusion
If we compare the p value and the significance level given for example we see that
so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.