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
Sonja [21]
3 years ago
7

Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing i

nterocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble polished using the first polishing solution, and of this number, 253 had no polishing-induced defects. Another 300 lenses were tumble-polished using the second polishing solution, and 196 lenses were satisfactory upon completion.
Is there any reason to believe that the two polishing solutions differ? Use α = 0.05. What is the P-value for this test?
Mathematics
1 answer:
Nina [5.8K]3 years ago
5 0

Answer:

z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358    

p_v =2*P(Z>5.358) = 4.2x10^{-8}  

Comparing the p value with the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.  

Step-by-step explanation:

Data given and notation  

X_{1}=253 represent the number with no defects in sample 1

X_{2}=196 represent the number with no defects in sample 1

n_{1}=300 sample 1

n_{2}=300 sample 2

p_{1}=\frac{253}{300}=0.843 represent the proportion of number with no defects in sample 1

p_{2}=\frac{196}{300}=0.653 represent the proportion of number with no defects in sample 2

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)  

\alpha=0.05 significance level given

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if is there is a difference in the the two proportions, the system of hypothesis would be:  

Null hypothesis:p_{1} - p_2}=0  

Alternative hypothesis:p_{1} - p_{2} \neq 0  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{253+196}{300+300}=0.748  

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358    

Statistical decision

Since is a two sided test the p value would be:  

p_v =2*P(Z>5.358) = 4.2x10^{-8}  

Comparing the p value with the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.  

You might be interested in
PLZZZZ HELPPPP!!!!!! 12 POINTS!!!
Paha777 [63]
Plug in each pair into each system of inequalities. And see which one fits
4 0
3 years ago
In order to meet ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no mor
r-ruslan [8.4K]

Check the picture below.

make sure your calculator is in Degree mode.

does it meet the requirements?  well, 3.43 < 4.8.

6 0
3 years ago
Read 2 more answers
Which category does each card go into?
WINSTONCH [101]

Step-by-step explanation:

E3, E6, E11, E7: no solution

E1, E12 : 1 solution

E2, E8, E10 : infinite solutions

7 0
3 years ago
Read 2 more answers
5g−2≤ 3g+8 3g+8<br><br> it says to solve for g.
Bess [88]

Answer:g is greater than or equal to 6g + 18/5, or g >_ 6g + 18/5

Step-by-step explanation: 5G- 2 <_ 6g + 16

Add 2 to the 16. 5g <_ 6g + 18.

Divide 5 to both sides. g >_ 6g + 18/5

7 0
2 years ago
Median for 9, 8, 5, 4, 3,18, 15 *<br><br><br>What is the mode for 1,1,1,2,3,5,10,10,10,10,14,11​
miskamm [114]

Answer:

median: 8

mode: 10

3 0
3 years ago
Other questions:
  • The plot below represents the function f ( x ) 1 2 3 4 5 -1 -2 -3 -4 -5 1 2 3 4 5 6 7 8 -1 -2 Evaluate f ( 1 ) f ( 1 ) = 4 Solve
    12·1 answer
  • A 4 ft by 8ft rectangle has a perimeter of _ft and an area of _ ft/2
    10·1 answer
  • Can someone help me with these coordinates (number two)
    8·2 answers
  • DOES ANYONE KNOW HOW TO DO THIS PROBLEM???? I AM NOT SURE HOW TO SOLVE THIS PROBLEM
    7·1 answer
  • Divide (2m3+7m2−6)÷(m−7)
    15·1 answer
  • Select the correct answer for when you evaluate the following function at f(5):
    13·2 answers
  • Part A
    15·1 answer
  • Could anyone help me solve this Algebra equation?
    9·1 answer
  • Can somebody help me on this
    11·1 answer
  • What is the numerical expression for 3 - 0 x 5 - 0 ?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!