To find left and rigth Riemann sum of
where
Here
So
Now divide the interval [1, 9] into
The subintervals are,
To find left Riemann sum use the left end points of the subintervals.
Here the left endpoints are, 1,
Now evaluate the function at left endpoints,
Substitute all values in the formula,
Therefore left Riemann sum is 223.
To find right Riemann sum.
The formula for right Riemann sum is,
Here
So
Now divide the interval [1, 9] into
The subintervals are,
In a study of the accuracy of fast food drive-through orders, Restaurant A had 298 accurate orders and 51 that were not accurate. a. Construct a 90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B:
In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 358 trials, the touch therapists were correct 172 times. Complete parts (a) through (d).
a) Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses? (Type an integer or a decimal. Do not round.)
b) Using Emily's sample results, what is the best point estimate of the therapists' success rate? (Round to three decimal places as needed.)
c) Using Emily's sample results, construct a
Round to three decimal places as needed - ?
Find a 95 confidence interval for based on inverting the test statistic statistic .
For our data we have
Therefore it can be proven that the MLE for is given by
To find the confidence interval I should invert the test statistic .
The most powerful unbiased size test for testing
where has acceptance region
Substituting my problem (I think) we get that the most powerful unbiased size test for testing
has acceptance region
or equivalently,
Substituting we obtain
This means that my confindence interval is defined to be
But I can't seem to find anything concrete and I feel that I've made mistakes somewhere. What to do?