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
6

Doctors nationally believe that 80% of a certain type of operation are successful. In a particular hospital, 47 of these operati

ons were observed and 37 of them were successful. At = .05, is this hospital's success rate different from the national average?
Mathematics
1 answer:
Ann [662]3 years ago
5 0

Answer:

z=\frac{0.787 -0.8}{\sqrt{\frac{0.8(1-0.8)}{47}}}=-0.223  

p_v =2*P(z  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of hospital's success rate is not significanlty different from 0.8 or 80%.  

Step-by-step explanation:

1) Data given and notation

n=47 represent the random sample taken

X=37 represent the operations successful

\hat p=\frac{37}{47}=0.787 estimated proportion of operations successful

p_o=0.8 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is different from 0.8 or 80%:  

Null hypothesis:p=0.8  

Alternative hypothesis:p \neq 0.8  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.787 -0.8}{\sqrt{\frac{0.8(1-0.8)}{47}}}=-0.223  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

p_v =2*P(z  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of hospital's success rate is not significanlty different from 0.8 or 80%.  

You might be interested in
Jerome's sister told him to multiply both the amount of water and the amount of drink
Akimi4 [234]

Step-by-step explanation:

i m not sure about this

have a nice day

3 0
2 years ago
Read 2 more answers
Does anyone know what the answer to this is?
pogonyaev

Answer:

154/18, simplified to 77/9.

Step-by-step explanation:


7 0
3 years ago
Denisa is saving for a new bicycle. The bicycle cost $89. So far, Denisa has earned $54 babysitting. What percent of the total c
xz_007 [3.2K]
$54/$89 means she has dared 60.6742% or you can round to 60.67%
5 0
3 years ago
Read 2 more answers
carrie has 340 marbles to put in the vase she wants the vases to either hold 100 marbles or 10 marbles which is the way she can
Elan Coil [88]

Carrie could have 3 vases filled with 100 marbles, and 4 vases filled with 10 marbles. Hope I helped!
4 0
3 years ago
Use differentials to estimate the amount of metal in a closed cylindrical can that is 26 cm high and 10 cm in diameter if the me
Afina-wow [57]

Answer:

The estimated amount of metal in the can is 87.96 cubic cm

Step-by-step explanation:

We can find the differential of volume from the volume of a cylinder equation given by

V= \pi r^2 h

Thus that way we will find the amount of metal that makes up the can.

Finding the differential.

A small change in volume is given by:

dV =\cfrac{\partial V}{\partial h} dh + \cfrac{\partial V}{\partial r} dr

So finding the partial derivatives we get

dV =\pi r^2 dh + \pi 2r h dr

dV =\pi r^2 dh + 2\pi r h dr

Evaluating the differential at the given information.

The height of the can is h = 26 cm, the diameter is 10 cm, which means the radius is half of it, that is r = 5 cm.

On the other hand the thickness of the side is 0.05 cm that represents dr = 0.05 cm, and the thickness on both top and bottom is 0.3 cm, thus dh = 0.3 cm +0.3 cm which give us 0.6 cm.

Replacing all those values on the differential we get

dV =\pi 5^2 (0.6) + 2\pi (5) (26) (0.05)

That give us

V= 28 \pi  \, cm^3

Or in decimal value

\boxed{dV= 87.96 \, cm^3}

Thus the volume of metal in the can is 87.96 cubic cm.

6 0
3 years ago
Other questions:
  • the length of a pool is 10 meters more than twice the width. The area of the pool is 1500 square meters. What is the length of t
    12·2 answers
  • Solve the inequality.<br> 2(4+2x)≥5x+5<br> A. x≤−2<br> B. x≥−2<br> C. x≤3<br> D. x≥3
    11·2 answers
  • Simplify the following expression
    14·1 answer
  • Rachel is setting up tables for a party. Four of the tables are covered with red tablecloths, and eight of the tables are covere
    14·1 answer
  • Which set of statements explains how to plot a point at the location
    15·1 answer
  • Which expression is equivalent to 7p+p+4p+2p−6? A 7p B 8p C 13p−6 D 14p−6
    11·1 answer
  • Round 796,154 to the nearest 1,000
    11·2 answers
  • Bu soruyu yapana 15 puan​
    6·2 answers
  • A number line going from 0 to 1. There are 6 equal spaces between 0 and 1. The line contains 0, A, B, blank, C, D, 1.
    6·2 answers
  • Or<br> Solve for q.<br> 5 – 4q ≤ –3
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!