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A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 100 items, th

pochemuha

Answer:

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

Step-by-step explanation:

A manufacturer considers his production process to be out of control when defects exceed 3%.

At the null hypothesis, we test if the production process is in control, that is, the defective proportion is of 3% or less. So

$H_0: p \leq 0.03$

At the alternate hypothesis, we test if the production process is out of control, that is, the defective proportion exceeds 3%. So

$H_1: p > 0.03$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.03 is tested at the null hypothesis

This means that $\mu = 0.03, \sigma = \sqrt{0.03*0.97}$

In a random sample of 100 items, the defect rate is 4%.

This means that $n = 100, X = 0.04$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.04 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{100}}}$

$z = 0.59$

P-value of the test

The p-value of the test is the probability of finding a sample proportion above 0.04, which is 1 subtracted by the p-value of z = 0.59.

Looking at the z-table, z = 0.59 has a p-value of 0.7224

1 - 0.7224 = 0.2776

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

4 0

3 years ago

What is the answer to 2 5/3-2 3/2=

jek_recluse [69]

First, we can convert both of them to improper fractions.

We do that by multiplying the denominator to the whole number, adding it to the numerator, and keeping the denominator.

2 5/3 - 2 3/2

So we have:

11/3 - 7/2

Convert both of them to denominators of 6:

22/6 - 21/6

Subtract the numerators and keep the denominators:

1/6

3 0

3 years ago

Read 2 more answers

Given that f(x)=2x^3+x-3, evaluate the function f(-2). A.) 11 B.) -69 C.) -21

prohojiy [21]

F(x)=2x³+x-3
f(-2)=2(-2)³+(-2)-3
f(-2)=2(-8)-2-3
f(-2)=-16-2-3
f(-2)=-18-3
f(-2)=-21. As a result,C is your final answer. Hope it help!

7 0

3 years ago

Read 2 more answers

Problem PageQuestion The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate paramet

asambeis [7]

Answer:

t = 1.51

Step-by-step explanation:

Exponential Model

The exponential model is often used to simulate the behavior of a magnitude that either grow or decay in proportion to the existing amount of that magnitude.

The model can be expressed as

$M=M_oe^{kt}$

In this case, Mo is the initial mass of the radioactive substance and k is a constant which value is positive if the mass is growing or negative if the mass is decaying.

The value of k is not precisely given in the question, we are assuming $k=-0.2$