A group of doctors published an article in the New England Journal of Medicine. In the article they revealed the findings of a study to determine if there is a difference in survival rates for men who undergo surgery for localized prostate cancer and those who are treated with observation only. The researchers randomly assigned 731 men with localized prostate cancer to radical prostatectomy or observation. During the years of follow-up, 245 of 367 (66.8%) assigned to surgery survived for at least 5 years and 223 of 364 men (61.3%) assigned to observation survived for at least 5 years.

Required:
a. Construct and interpret a 99% confidence interval for the difference in the true proportion of men like these that would survive for at least 5 years after receiving surgery and the proportion that would survive for at least 5 years when only being observed.
b. How does the confidence interval from part a tell you that there is not sufficient evidence at the a=.01 level that there is a difference in the proportion of men with localized prostate cancer who survive at least five years after receiving surgery and the proportion of men with localized prostate cancer who survive at least five years when only being observed. In other words, how would you know that the p-value for a 2 proportion z test would not be significant at the 0.01 level?

Answers

Answer 1

Answer:

a)  CI =  (  - 0,0352  ;  0,1472 )

b)  The CI  include 0 since that means we   don´t have sufficient evidence at α = 1 % to support differences between the two proportions

Step-by-step explanation:

From sample 1.    ( assigned to surgery)

sample size   n = 367

sample proportion   p₁  =  245/367    p₁  = 66,8 %   or p₁ = 0,668

Then  q₁ = 1 - 0,668   q₁ =  0,332

From sample 2.  ( assigned to observation )

sample size  n₂  = 364

sample proportion   p₂  =  223/364    p₂  = 61,2 %   or p₂ = 0,612

Then  q₂ = 1 - 0,612   q₁ =  0,388

Test Hypothesis is:

Null hypothesis                 H₀        p₂  =  p₁

Alternative Hypothesis    Hₐ        p₂ ≠ p₁

a) CI ( 99 %)     if  CI = 99%     significance level α = 1 %     α = 0,01

α/2 = 0,005  n z-table we look z (c) for  0,005

z(c)  = 2,578

CI    =              ( p₁  -  p₂  ) ± z(α/2) √(p₁*q₁) / n₁] + [ p₂*q₂/n₂

CI =(0,668 -0,612 ) ± 2,578 * √(0,668*0,332) /367 + (0,612*0,388)/364

CI = 0,056 ± 2,578*√6,04 *10⁻⁴ + 6,52 *10⁻⁴

CI = 0,056 ±  2,578*3,54*10⁻²

CI  = ( 0,056 - 0,0912 ;  0,056 + 0,0912 )

CI =  (  - 0,0352  ;  0,1472 )

b) The CI  include 0 since that means we   don´t have sufficient evidence at α = 1 % to support differences between the two proportions


Related Questions

PLEASE HELP!! Find the amount after 6 years if $1000 is invested at an annual rate of 4% compounded:
a) Annually
Amount - $
b) Semiannually
Amount $
c) Quarterly
Amounts
d) Monthly
Amount: $

Answers

B thank me later :) give me hearts


A line passes through the point (-8, -7) and has a slope of 5/4

Write an equation in slope intercept form for this line


Plzzz help

Answers

Answer:

y = 5/4x + 3

Step-by-step explanation:

Determine two pairs of polar coordinates for the point (12, 12) with 0° ≤ θ < 360°

Answers

Answer:

(12[tex]\sqrt{2}\\[/tex], 45°), (-12√2, 225°)

Step-by-step explanation:

....mhm

In full honesty though, this is the right answer

how to solve 13p-6=-33​

Answers

Answer:

The exact form: =- 27/13

Mixed number form = -2 1/13

Step-by-step explanation:

You move all of the terms that do not contain p to the right side and solve.

Answer:

use g00gle

Step-by-step explanation:

go to g00gle

hit the camera thing n  take a picture of yo problem

Please help me please !

Answers

Answer:

the one on the left is y=2/3x+1 and the one on the right is y=-4x+5

Step-by-step explanation:

Find the slope of the line.
1.
у
9
|(2,9)
6
(-1,3)
3
-2
o
1 2 3 x
6
9
Its graphing plss i need help

Answers

Answer:

The slope is 2

Step-by-step explanation:

Given

[tex](x_1,y_1) = (2,9)[/tex]

[tex](x_2,y_2) = (-1,3)[/tex]

Required

The slope (m)

This is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{3 - 9}{-1 - 2}[/tex]

[tex]m = \frac{- 6}{-3}[/tex]

[tex]m =2[/tex]

The Shoes cost $42
Each pack of socks costs $1.50
Martha has $53 to buy shoes and socks. If Martha buys one pair of shoes, what is the greatest number of packs of socks she can buy?

Answers

Answer:

Martha can buy 7 packs of socks.

Step-by-step explanation:

Martha has $53

Shoes = $42

Socks = $1.50 each

First subtract 42 from 53 to figure out how much is left:

⇒ $53 - $42 = $11

then divide the answer by how much each pack of socks cost:

⇒ [tex]\frac{11}{1.50}[/tex] = 7.33

next, take the whole number of the answer and multiply that by $1.50 to figure how much 7 pack of socks cost:

⇒ 7 socks x $1.50 = $10.50

subtract the answer from $11 to figure out how much remains:

⇒ $11 - $10.5 = $0.50

Answer:

She can buy 7 packs of socks

A number more than nine is more than twenty.

write as an inequality

Answers

Answer:

I think it is 20 < x > 9. But I am not completely sure.

Nicole bought a pair of shoes for
$37.93. The sales tax was $2.84. How
much money did Nicole spend on the
pair of shoes before taxes?

Answers

Answer:

$35.09

Step-by-step explanation:

37.93- 2.84= 35.09

Answer: 35.09$

Step-by-step explanation:

subtract the taxes from the total i think

Mr.Pope is buying Mrs. Pope's flowers. He buys 6 flowers for 10.95 without tax.
How much did he pay for each flower?

a. $2.00
b. $1.82
c. $1.825
d. $1.83

Answers

C

He payed $10.95 for 6 flowers. You want to find the price per each flower.

An equation to model this situation would be 6x = 10.95 where x = price per flower.

To solve this divide each side by 6.
10.95/6 = 1.825

Essentially to find the price per an individual thing you need to divide the total price by the amount of the item purchased.

He payed $1.825 per flower.
the answer is D because if you round the answer youll get 1.83

If c=1/3 and b=3 solve 3c divided by (2b to the 2nd power

Answers

Answer:

4 1/2

Step-by-step explanation:

3(1/3) divided by 2(3)2nd power

Christine is 4 years younger than Mark. 3 years from now, she will be two-thirds as old as Mark find their present ages.Complete solution​

Answers

Answer:Mark Is 9 years old; Christine is 5 years old

Step-by-step explanation:

Present age

LET  mark age be x

Christine be x-4 yrs

In 3 yrs Time

Mark will be x+3 yrs old

Christine  will be  (x -4 +3) = x-1 years old

Also, In 3 years time

Christine  = 2/3 Mark

such that

  x-1 = 2/3(x+3)

  x -1= 2x+6 / 3

    3x  -3= 2x+6

      3X--2X = 6+3

         =X=9

Mark Is 9 years old

Christine is   x -4 = 9-4=5 years old

g (15 points) Suppose 42 out of 600 rats exposed to a potential carcinogen develop tumors. A control group of 350 rats not exposed to the carcinogen develops 13 tumors. Based on these data, computed (a) the relative risk, (b) the attributable risk, and (c) the odds ratio. Do these indicators suggest that there is a relationship between exposure and tumor risk

Answers

Answer:

a) The relative risk is 1.8[tex]\overline{846153}[/tex]

b) The attributable risk is [tex]0.69 \overline{047619}[/tex]

c) There is a relationship between exposure and tumor risk

Step-by-step explanation:

The number of exposed rats that develop tumors, a = 42

The number of rats exposed to the carcinogen = 600 rats

The number of exposed rats that did not develop tumors, b = 600 - 42 = 558

The number of not exposed rats in the control group = 350 rats

The number of rats that develop tumors in the control group, c = 13 tumors

The number of not exposed rats that did not develop tumors, d = 350 - 13 = 337  rats

a) The relative risk, RR = a/(a + b)/(c/(c + d))

∴ RR = (42/(42 + 558))/(13/(13 + 337)) = 49/26 = 1.8[tex]\overline{846153}[/tex]

b) The attributable risk = (a - c)/a

∴ The attributable risk = (42 - 13)/42 = [tex]0.69 \overline{047619}[/tex]

c) The odds ratio = (a·b)/(c·d)

∴ The odds ratio = 42 × 558/(13 × 337) = 23439/4381 ≈ 5.35

Given that the result of attributable risk is positive, there is an indication that there is a higher probability to develop tumor when exposed to the potential carcinogen, therefore, there is a relationship between exposure and tumor risk

what is the sum of 6 1/2 + 2 1/3

Answers

Answer:

8 5/6

common denominator

Answer:

8 5/6

Step-by-step explanation:

Is this correspondence a function?

Answers

I’m not sure, sorry if I’m wrong but I’d say yes .

Explanation: A function is a correspondence between two sets where each element in the first set, called the domain, corresponds to exactly one element in the second set, called the range.
...

A quadrilateral has one pair of parallel sides with lengths 134 inches and 114 inches, and two angles that each measure 36°.

Answers

Answer:

Explanation:

1) The two parallel sides of different legths 1\frac{3}{4}143 and 1\frac{1}{4}141 constitute the bases of a trapezoid.

2) The two equal anglesare the base angles of the trapezoid, and mean that it is an isosceles trapezoid.

An isosceles trapezoid is truncated isosceles triangle.

The definition of trapezoid is a quadrilateral with at least two parallel sides.

The drawing is attached: only the green lines represent the figure, the dotted lines just show how this is derived from an isosceles triangle.

Item 13
Write an explicit rule for the recursive rule.

$a_1=16,a_n=0.5a_{n-1}$

Answers

Answer:

Step-by-step explanation:

[tex]a_{1}=16[/tex]

[tex]r=\frac{a_{n}}{a_{n-1}} =0.5\\a_{n}=a_{1}r^{n-1}=16(0.5)^{n-1}[/tex]

Write the 0.5% in two other forms (fraction and percent).

Answers

You can use 5/10 and 50% which is the same as 0.5%

Rewrite the funtion of f(x)=5(x-4)^3 + 6 with y instead of x

Answers

Answer:

f(y)=5(y-4)^3 + 6

Step-by-step explanation:

Given that

f(x)=5(x-4)^3 + 6

Now we have to rewrite the above function and put y in place of x

i.e.

f(y)=5(y-4)^3 + 6

Therefore the above represent the function in y form

Hence, the same would be relevant

NEED HELP ON THIS ASAP

Answers

Answer:

CosF=A/H

CosF=24/25

CosF=0.96

F=Cos^-1(0.96)

F=16°

4. According to the graph above, which of
the following best represents the number of
calories from protein a person on a 2,200-
calorie diet should consume?
A. 450
B. 550
C. 625
D. 650

Answers

The answer to this is D!!!!

Answer: B:550.                  You do percent over 100 equals part over whole.you put 25 as your percent over 100 then you put 2,200 as your whole put x on part then you multiply 25x2,200=55,000 then you dived 55000 and 100 and you get 550

Stacia randomly chooses a number from 1 to 10. What is the probability she
chooses a number less than 4?

Answers

Answer:

The probability that she chooses a nuumber less than 4 is 30%

Step-by-step explanation:

Find the area of the figure.
A)41 cm
B)90 cm
C)95cm
D)100cm

Answers

Answer:

The answer is B) 90 cm^2

Step-by-step explanation:

The area of the rectangle and the triangle are

[tex]rect = 10 \times 8 =80 \\ tria = 0.5 \times 4 \times 5 = 10 \\ the \: total \: area \: is \: 80 + 10 = 90[/tex]

I hope that is useful for you

The stem-and-leaf plot represents the distances, in miles, people in an office drive to work each morning.

How many people drive 20 miles or fewer to work?



Enter your answer in the box.

A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 6, 6, 7, 7, 8, 8, a stem value of 2 with a leaf value of 1, 4, 5, 9, and a stem value of 3 with a leaf value of 0, 5, 5, 6.

Key: 1|5 means 15

Answers

Answer:

8

Step-by-step explanation:

The x-coordinates of the points (112,−3) and (112,3) are the same and their y-coordinates are opposites. What does this mean in terms of the positions of the points?

Answers

Answer:

They are reflected across the x-axis

Step-by-step explanation:

What's the value of (5³)¹. I need a explanation.​

Answers

Answer:

125

Step-by-step explanation:

We can first multiply the exponent outside the parentheses by the exponent inside the parentheses.

3*1 = 3.

Now we can solve.

5³ = 125

And there is your answer. Hope this helps. Have a nice day.

PLS HELP!!! Angle 3 and Angle 8 are congruent
True or false

Answers

Answer:

false

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

something congruent is similar in shape

How many solutions does the nonlinear system of equations graphed below have

Answers

Answer:

C. two

Step-by-step explanation:

2 points of intersection

Option C is correct, there are two solutions to the nonlinear system of equations graph.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A system of nonlinear equations is a system of two or more equations in two or more variables containing at least one equation that is not linear.

In this case, we have a parabola (the red figure) and a line (the blue figure).

There are three possible types of solutions for a system of nonlinear equations involving a parabola and a line.

No solution. The line will never intersect the parabola.

One solution. The line is tangent to the parabola and intersects the parabola at exactly one point.

Two solutions. The line crosses on the inside of the parabola and intersects the parabola at two points.

Hence, there are two solutions to the nonlinear system of equations graph.

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ7

D. Problem Solving
11.
A paper balloon costs Php 7.50. What is the cost if I buy 6 balloons?
Solution:
12. My Auntie bought 3 kg of pork and 2.5 kg of chicken. If the pork costs Php110.50 per
chicken?
kilogram and she spent a total of Php580.00, how much did she pay for a 2.5 kg of
Solution:
13.
Item A costs Php22.50 per kilogram and item B costs Php18.25 per kilogram. Which costs less
Solution:
14. Marianne pays Php79.85 each month as membership cost to her gym. How much money does
she pay annually?
Solution:
15. Gary surveyed his classmates at the school and found out that they play sports for about 3.8
hours per week. About how many hours do his classmates spend while playing sports in a year that has 52 Weeks?
Solution

that has 52 weeks?
kg of o​

Answers

Answer:

11. P7.50 x6 = P45.00

12 P580 - (P110.50 x 3) = P 580 - P 331.5 = P248.50

13. Item B costs less

14. P79.85 x12 months = P958.20

15. Given: 3.8 hours per week

52 weeks x 3.8 hours = 197.6 hours

i don't get how to do this one

Answers

Its the second one............
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