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
Date:
Vlad [161]

Answer:

He should enter the lottery

Step-by-step explanation:

8 0
3 years ago
What is the simplified base of the function f(x) = 1/4 3/108*x?
Zinaida [17]
The Answer is B. 3 x 3/4
4 0
3 years ago
Read 2 more answers
Please please someone help
natka813 [3]

The answer is the first one:

bc its not growing by a (-)1/2  and the 3rd one just doesnt make sense

7 0
3 years ago
Read 2 more answers
To start, which measurement does Tommy need to
Luba_88 [7]

Answer:

C. volume

Step-by-step explanation:

when youre starting your measurements you want to start the volume first.

8 0
3 years ago
Read 2 more answers
In 56 years,Kevin will be 9 times as old as he is right now . <br> How old is he right now ?
grandymaker [24]
6 bc if you divide 56 by 9 you’ll get 6.2 but i’m not sure the ( .2 ) will matter therefore just get the first digit which is 6
8 0
3 years ago
Read 2 more answers
Other questions:
  • What do you divide -81 to get +81?
    7·1 answer
  • Finding the Zeros
    9·2 answers
  • A line passes through the point (0, –1) and has a slope of -2/3 What is the equation of the line?
    12·1 answer
  • I need help on this question
    6·1 answer
  • When 27 times x squared times z all over negative 3 times x squared times z to the sixth power is completely simplified, the exp
    10·1 answer
  • What is the total area? Use 3 for Pi.<br> Answer fast pls!! xx
    9·2 answers
  • How do you write 1.52 × 101 in standard form?
    8·1 answer
  • Which is a better estimate for the volume of a shoebox? 5) 4 liters 4 milliliter​
    6·1 answer
  • Michael went to the grocery store and bought bottles of soda and bottles of juice.
    6·1 answer
  • Please help with question with explanations. Ty.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!