A direct mailing company sells computers and computer parts by mail. The company claims that at least 90% of all orders are mailed within 72 hours after they are received. The quality control department at the company often takes samples to check if this claim is valid. A recently taken random sample of 150 orders showed that 129 of them were mailed within 72 hours. Set up the null and alternative hypotheses to test whether the company’s claim is true?

Answers

Answer 1

Answer:

Answer:

The null and alternative hypothesis are:

$H_0: \pi=0.9\n\nH_a:\pi<0.9$

There is not enough evidence to support the claim that the company is worng and less than 90% of all orders are mailed within 72 hours after they are received.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The company claims that at least 90% of all orders are mailed within 72 hours after they are received. The company's claim is the null hypothesis, the claim that is going to be tested is if this proportion is significantly less than 90%.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.9\n\nH_a:\pi<0.9$

The significance level is 0.05.

The sample has a size n=150.

The sample proportion is p=0.86.

$p=X/n=129/150=0.86$

The standard error of the proportion is:

$\sigma_p=\sqrt{(\pi(1-\pi))/(n)}=\sqrt{(0.9*0.1)/(150)}\n\n\n \sigma_p=√(0.0006)=0.024$

Then, we can calculate the z-statistic as:

$z=(p-\pi+0.5/n)/(\sigma_p)=(0.86-0.9+0.5/150)/(0.024)=(-0.037)/(0.024)=-1.497$

This test is a left-tailed test, so the P-value for this test is calculated as:

\text{P-value}=P(z<-1.497)=0.0672

As the P-value (0.0672) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 90% of all orders are mailed within 72 hours after they are received.

Answer 2

Answer:

Final answer:

The null hypothesis is that 90% of all orders are shipped within 72 hours, denoted as H0: p = 0.90. The alternative hypothesis is that less than 90% of all orders are shipped within 72 hours, expressed as HA: p < 0.90.

Explanation:

In hypothesis testing, the null hypothesis represents the theory that has been put forward, either because it is believed to be true or because it is used as a basis for argument. In this case, the null hypothesis would be that 90% of all orders are shipped within 72 hours. This can be formulated as H0: p = 0.90 where p represents the proportion of all orders shipped within 72 hours.

The alternative hypothesis on the other hand is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. Here, the alternative hypothesis would be that less than 90% of all orders are shipped within 72 hours. It can be expressed as HA: p < 0.90 where p remains the proportion of orders shipped within 72 hours.

Learn more about Hypothesis Testing here:

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01) What is the perimeter of shape B?
2) Which shape's perimeter is less? Shape A or shape D.
3) Area of which shape is more?
4) Area of which shapes are equal?
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Answers

Answer:

whichshape's permeteris less shape A or D shape.

Answer:

ask google assistaint then if you dont get it go f yourself like u did to me

Step-by-step explanation:

What is the square footage of 9.5 feet x 12 feet

Answers

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Rosa graphs the line y = 3x + 5.then she dilates the line by a factor of 1/5 with (0,7) as the center of dilation .

Answers

The equation of the dilated line is y = (3/5)x + (33/5), and it passes through the point (0,7).

How to measure dilation?

To dilate the line y = 3x + 5 by a factor of 1/5 with (0,7) as the center of dilation, we can follow these steps:

Shift the line so that the center of dilation is at the origin. To do this, we subtract 7 from the y-intercept of the original line, giving us y = 3x - 2.

Apply the dilation factor to the line. To do this, we multiply the coordinates of each point on the line by 1/5. This gives us the new equation:

y = (3/5)x - (2/5)

Shift the line back to its original position. To do this, we add 7 to the y-intercept of the dilated line, giving us the final equation:

y = (3/5)x + (33/5)

Therefore, the equation of the dilated line is y = (3/5)x + (33/5), and it passes through the point (0,7).

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Answer:

Different slope of 3

Step-by-step explanation:

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The height of a cylinder is decreasing at a constant rate of 1 centimeters per minute, and the volume is decreasing at a rate of 2341 cubic centimeters per minute. At the instant when the height of the cylinder is 1010 centimeters and the volume is 577 cubic centimeters, what is the rate of change of the radius? The volume of a cylinder can be found with the equation V=pi r^2 h. Round your answer to three decimal places.

Answers

Let's organize our given information.

$(dh)/(dt)=-1$

$(dV)/(dt)=-2341$

$(dr)/(dt)=?, h=1010, V=577$

$V=\pi r^2h$

What I'd like to do is solve for $r$ first, it'll help later.

$577=\pi r^2(1010)$

$r=\sqrt{(577)/(1010\pi)}$

$r=0.426$

Now, we can differentiate our formula for the volume of a cylinder to find the rate of change of the radius.

$V=\pi r^2h$

Use the product rule of differentiation.

$(dV)/(dt)=2\pi rh(dr)/(dt)+\pi r^2(dh)/(dt)$

Plug in the information we are given.

$-2341=2\pi (0.426)(1010)(dr)/(dt)+\pi (0.426)^2(-1)$

Solve for $(dr)/(dt)$ .

$-2341=860.52\pi(dr)/(dt)+(0.426)^2\pi$

$-2341.57=860.52\pi(dr)/(dt)$

$(dr)/(dt)=-0.866$

The rate of change of the radius is -0.866 centimeters per minute.

Hope this helps!

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Answers

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Ok if Dan made 1412.42 and Aaron made 1187.92 And total amount of fuel for the truck was 418.91 how do fuel do I deduct for each driver? They both driving the same truck. I need to know how to divide the fuel evenly

Answers

First we should calculate the relation between how much they make and the fuel cost so we write

(1412.42+1187.92)/418.91=6.21

So that means that for every 6.21 dollars made 1 dollar of fuel must be deducted so now we calculate what they need to be deducted by:

Dan deduction = 1412.42/6.21= 227.41
Aaron deduction= 1187.92/6.21 = 191.29

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