Mathematics, 16.11.2020 16:50 krystabrewer3

A sample of 12001200 computer chips revealed that 53S% of the chips do not fail in the first 10001000 hours of their use. The company's promotional literature claimed that more than 50P% do not fail in the first 10001000 hours of their use. Is there sufficient evidence at the 0.100.10 level to support the company's claim

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Answer from: smthcrm

Complete Question

A sample of 1200 computer chips revealed that 53% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that more than 50% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.10 level to support the company's claim

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to conclude that the company's promotional literature claimed that more than 50% do not fail in the first 1000 hours of their use is correct

Step-by-step explanation:

From the question we told that

The sample size is n = 1200

The significance level is $\alpha = 0.100$

The sample proportion is $\^ p = 0.53$

The null hypothesis H_o : p = 0.50

The alternative hypothesis is Ha : p 0.50

Generally the test statistics is mathematically represented as

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

=> $z = \frac{ 0.53 - 0.5 }{ \sqrt{\frac{0.50 (1 - 0.50)}{1200} } }$

=> z = 2.078

From the z table the area under the normal curve to the right corresponding to 2.078 is

P(Z 2.078 ) = 0.018855

p-value = 0.018855

Generally the value obtained we see that $p-value < \alpha$ , Hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to conclude that the company's promotional literature claimed that more than 50% do not fail in the first 1000 hours of their use is correct

Answer from: Quest

answer: 5000

step-by-step explanation:

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

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