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ruslelena [56]
3 years ago
10

A manufacturer claims that fewer than 6% of its fax machines are defective. to test this claim, he selects a random sample of 97

such fax machines and finds that 5% are defective. find the p-value for the test of the manufacturer's claim. 0.1591

Mathematics
1 answer:
AfilCa [17]3 years ago
3 0

Let P be the population proportion, p be the sample proportion, n be the sample size.

A manufacturer claims that fewer than 6% of its fax machines are defective. It means P=0.06

Sample size n=97 and sample proportion p=0.05

The hypothesis to be tested is

H0: P ≥ 0.06 V/s Ha: P < 0.06

Here the hypothesis for testing population proportion we use z test statistics. Z test statistics is give by

Z = \frac{p -p_{0}}{\sqrt{p_{0}(1-p_{0})/n}}

Where p =sample proportion = 0.05

p0 = hypothesized proportion value =0.06

Using given values into test statistics we get

Z = \frac{0.05 -0.06}{\sqrt{0.06(1-0.06)/97}}

Z = -0.41

The p-value for left tailed alternative hypothesis is given by

P-value = P(z < z cal)

where zcal = Z test statistics value

Here zcal = -0.41

P-value = P(Z < -0.41)

Using z score table to find probability below z=-0.41

P-value = 0.3409

P-value for testing the given claim is 0.3409

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Doing factorization, we know that the factors of the given equation are ±√5 and ±10i.

<h3>What is Factorization?</h3>

In mathematics, factorization or factoring consists of writing a number or any mathematical item as a product of several factors, typically small or easier objects of the same.

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So, we have the equation:

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Know more about Factorization here:

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Complete question:
What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.

x=+- sqrt 5 and x = ±10

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x=+- sqrt 5 and x = ±10i

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<u />

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