Mathematics: A sample of 1600 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. The company s promotional literature claimed that over 31% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company s claim

Step-by-step explanation:Equation of a circle is given as : Take the derivative of the above with respect to xThe equation of the tangent is given by :...

A sample of 1600 computer chips revealed that - id16003410436795, alphaaz23415

Ответ:

colrow1968

17.03.2022

Mathematics

Answer is given below:

Step-by-step explanation:

given data

sample n = 1600

P = 34 %

p = 31 %

solution

The null and alternative hypothesis are

H0: p = 0.31

Ha: p > 0.31

Test statistics

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

z = 0.34 - 0.31 $\sqrt{( 0.31 \times 0.69 / 1600)}$

z = 2.59

This is test statistics value.

p-value = P( Z > z)

p-value = P( Z > 2.59)

p-value = 0.0048

Since p-value < 0.05

level, we have sufficient evidence to reject H03

We conclude at 0.05 level that we have enough evidence t support the claim.

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Ответ:

emilypzamora11

26.01.2020

Mathematics

y = -0.75x + 9.5

Step-by-step explanation:

Equation of a circle is given as :

$(x-a)^{2} + (y-b)^2 = r^{2} \\(x-6)^{2} + (y-5)^2 = 4^{2}\\x^{2} - 12x + 36 + y^{2} -10y + 25 = 16\\x^{2} - 12x + y^{2} -10y + 45 = 0\\$

Take the derivative of the above with respect to x

$2x - 12 + 2y dy/dx - 10 dy/dy = 0\\\frac{dx}{dy} = \frac{6 - x}{y-5} \\At (2,8) dy/dx = (6-2)/(8-5) = 4/3\\dy/dx = 4/3\\The slope of the tangent to the circle, m = \frac{-1}{dy/dx} \\m = \frac{-1}{4/3}\\m= -0.75$

The equation of the tangent is given by :

$y - y_{1} = m(x - x_{1})\\ y - 8 = -0.75(x - 2)\\y - 8 = -0.75x + 1.5\\y = -0.75x + 9.5$

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A sample of 1600 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that over 31% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim

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