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Hoochie [10]
3 years ago
15

A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a randomsample of 600 disks, it is found tha

t 3% are defective, but the supplier claims that this isonly a sample fluctuation. At the 0.01 level of significance, do the data provide sufficientevidence that the percentage of defects exceeds 1%
Mathematics
1 answer:
olga55 [171]3 years ago
4 0

Answer:

At a significance level of 0.01, there is enough evidence to support the claim that the percentage of defective disks exceeds 1%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of defective disks exceeds 1%.

Then, the null and alternative hypothesis are:

H_0: \pi=0.01\\\\H_a:\pi>0.01

The significance level is 0.01.

The sample has a size n=600.

The sample proportion is p=0.03.

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.01*0.99}{600}}\\\\\\ \sigma_p=\sqrt{0.000017}=0.004

Then, we can calculate the z-statistic as:

z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.03-0.01-0.5/600}{0.004}=\dfrac{0.019}{0.004}=4.719

This test is a right-tailed test, so the P-value for this test is calculated as:

P-value=P(z>4.719)=0.000001

As the P-value (0.000001) is smaller than the significance level (0.01), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the percentage of defective disks exceeds 1%.

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The height of a ball thrown into the air after t seconds have elapsed is h = −16t2 + 40t + 6 feet. What is the first time, t, wh
sp2606 [1]
<h3>The first time when the ball will reach a height of 20 feet is 0.42 seconds</h3>

<em><u>Solution:</u></em>

Given that,

<em><u>The height of a ball thrown into the air after t seconds have elapsed is:</u></em>

h = -16t^2 + 40t + 6

<em><u>What is the first time, t, when the ball will reach a height of 20 feet?</u></em>

Substitute h = 20

20 = -16t^2 + 40t + 6\\\\-16t^2 + 40t + 6 -20 = 0\\\\-16t^2 + 40t -14 = 0\\\\16t^2 -40t + 14 = 0\\\\8t^2 -20t + 7=0

<em><u>Solve by quadractic formula</u></em>

\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

\mathrm{For\:}\quad a=8,\:b=-20,\:c=7

t = \frac{-\left(-20\right)\pm \sqrt{\left(-20\right)^2-4\cdot \:8\cdot \:7}}{2\cdot \:8}\\\\t = \frac{20 \pm \sqrt{176}}{16}\\\\t = \frac{20 \pm 4\sqrt{11}}{16}\\\\t = \frac{ 5 \pm \sqrt{11}}{4}\\\\We\ have\ two\ solutions\\\\ t=2.07915, \:t=0.42084

Rounding off we get,

t = 2.08 , t = 0.42

Thus the first time when the ball will reach a height of 20 feet is 0.42 seconds

4 0
3 years ago
Find the x -intercept of the line whose equation is 10 x + 3 y = 1. <br> 1/3 <br> 1/10<br> 1
prisoha [69]

the answer 1/10 hope that is correct



3 0
3 years ago
Read 2 more answers
I
atroni [7]

Answer: 16⅔ yds by 25 yds

Step-by-step explanation:

Let x be the length of 3 fence sections

Let y be the length of 2 fence sections

A = xy

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y = 50 - 1.5x

A = x(50 - 1.5x) = 50x - 1.5x²

dA/dx = 50 - 3x

       0 = 50 - 3x

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        x = 50/3 = 16⅔ yds

        y = 50 - 1.5(16⅔) = 25 yds

5 0
3 years ago
I'm so confused to this problem someone please help me ​
svetoff [14.1K]

(xy)⁷

=(x⁷)(y⁷)

This is the simplified term.

4 0
2 years ago
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inysia [295]
For Beth, we know that she works 5 days a week and that she earns $54 dollars per day. Next, add the $10 dollars for each extra hour of work. p stands for the amount she gets paid.
(54 * 5) + (10 * x) = p
 
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(60 * 5) + (8 * x) = p 
6 0
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