Ahealthcare provider monitors the number of cat scans performed each month in each of its clinics. the most recent year of data for a particular clinic follows (the reported variable is the number of cat scans each month expressed as the number of cat scans per thousand members of the health plan): 2.31 2.09 2.36 1.95 1.98 2.25 2.16 2.07 1.88 1.94 1.97 2.02 (a) find a 95% two-sided confidence interval on the mean number of cat scans performed each month at this clinic. (b) historically, the mean number of scans performed by all clinics in the system has been 1.95. is there any evidence that this particular clinic performs more cat scans on overage than the overall system average?

a) 95% two-sided confidence interval on the mean number of CAT scans is

between 1.98 and 2.18

b) Yes. In 95% confidence, the particular clinic outperform than the overall system average.

Step-by-step explanation:

(a)

Confidence interval can be calculated as M±ME where

and margin of error (ME) around the mean can be found using the formula

ME= where

Using the numbers ME= ≈ 0.095

Confidence interval is then 2.08±0.095

(b) since the 95%confidence interval is higher than 1.95, the clinic outperforms.

can you hlep me do homework?

step-by-step explanation:

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!