Please someone help me

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines

storchak [24]

Answer:

The null hypothesis is $H_o: \mu = 4$ .

The alternate hypothesis is $H_a: \mu \neq 4$

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

Step-by-step explanation:

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.

This means that the null hypothesis is that they are 4.00 cm long, that is:

$H_o: \mu = 4$

At the alternate hypothesis we test if it is different. So

$H_a: \mu \neq 4$

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.

4 is tested at the null hypothesis:

This means that $\mu = 4$

After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm.

This means that $n = 196, X = 4.14$

He knows that the population standard deviation is 0.83 cm.

This means that $\sigma = 0.83$

Value of the test statistic:

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

$z = \frac{4.14 - 4}{\frac{0.83}{\sqrt{196}}}$

$z = 2.36$

Pvalue of the test and decision:

The pvalue of the test is the probability that the sample mean is different by at least 4.14 - 4 = 0.14 from the target value, which is P(|z| > 2.36), which is 2 multiplied by the pvalue of z = -2.36.

Looking at the z-table, z = -2.36 has a pvalue of 0.0091

2*0.0091 = 0.0182

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

5 0

3 years ago

Factor the polynomial expression 27x^6-8

Sedaia [141]

Answer:

(3 x 2 − 2) (9 x 4 + 6 x 2 + 4)

Step-by-step explanation:

I attached a screenshot that explains more

May I ave brainliest please? :)

5 0

3 years ago

A person gets on a Ferris wheel at the starting point. The starting point is 15 feet off the ground. The Ferris wheel has a radi

lisov135 [29]

<h2>Answer:</h2>

$\boxed{\frac{25}{2}(\sqrt{6}+\sqrt{2})+65}$

<h2>Explanation:</h2>

<em>The height of the rider from the ground after the Ferris wheel</em> equals <em>the starting point is 15 feet off the ground </em><em>plus </em><em>the radius of the Ferris wheel </em><em>plus </em><em>the opposite side of the triangle ΔABC </em>(See figure below).<em> </em>Hence our goal is to find this side. We have the angle $11\pi /2=165^{\circ}$ , therefore the angle ∠BAC = 165° - 90° = 75°. So this side can be found using trigonometry: