1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Paraphin [41]
3 years ago
14

A healthcare 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 CI 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. If there any evidence that this particular clinic performs more CAT scans on average than the overall system average?
Mathematics
1 answer:
Rasek [7]3 years ago
8 0

Answer: a. 1.981 < μ < 2.18

              b. Yes.

Step-by-step explanation:

A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.

First, we calculate mean of the sample:

\overline{x}=\frac{\Sigma x}{n}

\overline{x}=\frac{2.31=2.09+...+1.97+2.02}{12}

\overline{x}= 2.08

Now, we estimate standard deviation:

s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }

s=\sqrt{\frac{(2.31-2.08)^{2}+...+(2.02-2.08)^{2}}{11} }

s = 0.1564

For t-score, we need to determine degree of freedom and \frac{\alpha}{2}:

df = 12 - 1

df = 11

\alpha = 1 - 0.95

α = 0.05

\frac{\alpha}{2}= 0.025

Then, t-score is

t_{11,0.025} = 2.201

The interval will be

\overline{x} ± t.\frac{s}{\sqrt{n} }

2.08 ± 2.201\frac{0.1564}{\sqrt{12} }

2.08 ± 0.099

The 95% two-sided CI on the mean is 1.981 < μ < 2.18.

B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.

You might be interested in
A pair of shoes that normally sells for $82.88<br> goes on sale for 35% off. What is the sale price?
Alex17521 [72]

Answer:

The price would be $53.88

Step-by-step explanation:

Do $82.88*0.35=29

82.88-29=53.88

Hoped this Helped

7 0
3 years ago
Read 2 more answers
What is 712 divided by 8
sergeinik [125]
712 divided by 8 is 89
4 0
3 years ago
Read 2 more answers
Help!!<br> f (x) =-3x+25; Find f(x)=52
melamori03 [73]
<h3>Solution for -3x+25=52 equation:</h3>

Simplifying

-3x + 25 = 52

Reorder the terms:

25 + -3x = 52

Solving

25 + -3x = 52

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-25' to each side of the equation.

25 + -25 + -3x = 52 + -25

Combine like terms: 25 + -25 = 0

0 + -3x = 52 + -25

-3x = 52 + -25

Combine like terms: 52 + -25 = 27

-3x = 27

Divide each side by '-3'.

x = -9

Simplifying

x = -9

4 0
2 years ago
What dose this equal -7/8+(-5/8)
Levart [38]

Answer:

-12/8 or -1.5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Hat is the solution to the system of equations?
Dima020 [189]

Answer:

(–19, 55)

Step-by-step explanation:

y = –3x – 2   equation 1

5x + 2y = 15 equation 2

using equation 1 in equation 2 we have:

5x + 2(–3x – 2) = 15

5x –6x – 4 = 15

-x = 15+4

x=-19

using equation 1:

y = -3(-19)- 2  

y= 57-2

y= 55

5 0
3 years ago
Other questions:
  • Help ASAP I will give a thanks and 5 stars
    15·1 answer
  • Given that ABCD is a rhombus, what is the value of x?
    14·1 answer
  • A portable music player has 2 gigabytes of storage and can hold about 500 songs. A similar but larger media player has 80 gigaby
    12·1 answer
  • If the centroid of the triangle formed by (x,0), (5.2) and (-8.y) is at (-2,1) then (x,y) is equal to
    10·1 answer
  • What is the solution of 7k+2=4k-10?
    15·1 answer
  • Someone plss help plss helppp plllsss Will mark brainliestSomeone plss help plss helppp plllsss Will mark brainliestSomeone plss
    12·1 answer
  • Help me pls offering good points
    10·1 answer
  • How can you use 260 divided by 13 to help you find 286 divided by 13
    6·1 answer
  • What is the area of the circle below? Use 3.14 for pi?
    11·2 answers
  • Help how would you do this?<br>-3x + 16 =1​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!