Use picture

From 19 measurements of a pressure controller, the mean operating pressure is 4.97 kPa with a standard deviation of 0.0461 kPa.

Semenov [28]

Answer:

$4.97-2.10\frac{0.0461}{\sqrt{19}}=4.95$

$4.97+2.10\frac{0.0461}{\sqrt{19}}=4.99$

So on this case the 95% confidence interval would be given by (4.95;4.99)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X =4.97$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.0461 represent the sample standard deviation

n=19 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=19-1=18$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that $t_{\alpha/2}=2.10$

Now we have everything in order to replace into formula (1):

$4.97-2.10\frac{0.0461}{\sqrt{19}}=4.95$

$4.97+2.10\frac{0.0461}{\sqrt{19}}=4.99$

So on this case the 95% confidence interval would be given by (4.95;4.99)

5 0

3 years ago

Two sides of a trapezoidal are 25 meters. The third side is 40 meters. The fourth side is 20 meters shorter than the longest sid

Aloiza [94]

Answer:

110

Step-by-step explanation:

longest side would by 40 so 40 - 20 = 20. Add all the sides up 25+25+40+20=110

3 0

3 years ago

How to set up a system of equations

Scorpion4ik [409]

To set up your system of equations is to have 2 equations. They both would have 1 similar variable. For example, Jenny is 5 more her brother's age. She is also 2 more than twice her brother's age. You would set this up as Y, which is Jenny, and X, her brother. Y = 5 + x and Y = 2x + 2. Make sure you put Y in the same spot in both equations. Then take the other half of the equations and simplify them. 5 + x = 2x + 2. Subtract x from both sides to get 5 = x + 2. Subtract 2 from both sides to get 3 = x. Now replace the X from both equations to get Y = 5+3, and Y = 2(3) + 2. You will see both add up to 8, which is how old Jenny is in this example. Hope this helped!

4 0

3 years ago

And activating the<br> body to respond to information received.<br> I

Eduardwww [97]

Answer:

What?

Step-by-step explanation:

3 0

3 years ago

What is 0.973.. as a fraction

Artyom0805 [142]

Well, since it has 3 numbers not including the 0, we could change it to 973/1000.