WILL GIVE BRILLIANTIEST!

A journal article reports that a sample of size 5 was used as a basis for calculating a 95% CI for the true average natural freq

oksano4ka [1.4K]

Answer:

$Lower = 231.134- 3.098=228.036$

$Upper = 231.134+ 3.098=234.232$

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=5 represent the sample size

Solution to the problem

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

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

And for this case we know that the 95% confidence interval is given by:

$\bar X=\frac{233.002 +229.266}{2}= 231.134$

And the margin of error is given by:

$ME = \frac{233.002 -229.266}{2}= 1.868$

And the margin of error is given by:

$ME= t_{\alpha/2} \frac{s}{\sqrt{n}}$

The degrees of freedom are given by:

$df = n-1 = 5-1=4$

And the critical value for 95% of confidence is $t_{\alpha/2}= 2.776$

So then we can find the deviation like this:

$s = \frac{ME \sqrt{n}}{t_{\alpha/2}}$

$s = \frac{1.868* \sqrt{5}}{2.776}= 1.506$

And for the 99% confidence the critical value is: $t_{\alpha/2}= 4.604$

And the margin of error would be:

$ME = 4.604 *\frac{1.506}{\sqrt{5}}= 3.098$

And the interval is given by:

$Lower = 231.134- 3.098=228.036$

$Upper = 231.134+ 3.098=234.232$

6 0

3 years ago

If 2a+4b=5 and a is equal to three times b, what is 3a?

IrinaK [193]

Answer:

3a=4.5

Step-by-step explanation:

it says that "a is equal to 3 times b", which translates to a=3b

We can substitute a as 3b in 2a+4b=5

2(3b)+4b=5

multiply

6b+4b=5

add

10b=5

divide by 10

b=1/2

since it's given that a=3b, we can multiply 1/2 by 3

a=3/2

3a is 3 times a, so we can mutiply 3(3/2)=9/2=4.5

Hope this helps!

7 0

2 years ago

A stick 7 inches long is broken into two pieces, so that one piece is twice as long as the other one. How long are the two piece

marshall27 [118]

Hello from MrBillDoesMath!

Answer:

7/3 and 14/3 inches

Discussion:

Let P1 = "Piece 1" and "P2 = Piece 2", Then P2 = 2 * P1 and

P1 + P2 = 7 => as P2 = 2 P1

P1 + 2P1 = 7 =>

3P1 = 7 => divide both sides by 7

P1 = 7/3

Then P2 = 2 P1 - 2* (7/3) = 14/3

Thank you,

MrB

7 0

3 years ago

Read 2 more answers

Which ofnthe following shows the correct use of distributive property when solving 1/3(33-x)=135,2

madam [21]

Answer: OPTION C.

Step-by-step explanation:

The missing options are:

$A. (33 - x) = \frac{1}{3} * 135.2\\\\B. (\frac{1}{3} *33) - \frac{1}{3} x = \frac{1}{3} * 135.2\\\\C.(\frac{1}{3} * 33) - \frac{1}{3} x = 135.2\\\\D. (\frac{1}{3} * 33) + \frac{1}{3} x = 135.2$

In order to solve this exercise you need to remember the following:

1. The Distributive property states that:

$a(b+c)=ab+ac\\\\a(b-c)=ab-ac$

2. The multiplication of signs:

$(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-$

In this case the exercise gives you the following equation:

$\frac{1}{3}(33-x)=135.2$

Since you need to solve for the variable "x" in order to find its value, the first step you must apply in the in the procedure is to eliminate the parentheses applying the Distributive property.

Then, you must multiply everyting inside the parentheses by $\frac{1}{3}$ .

Therefore,based on the explanation, you know that the correct use of the Distributive property is:

$\frac{1}{3}*33-\frac{1}{3}x=135.2$

8 0

3 years ago

eight-two students are in the math club .35 students are in the science club .How many more students are in the math club than s

arsen [322]

There are 47 more because we are find “less” so we subtract to find the answer. 82-35=47

3 0

3 years ago