HELPPP, ASAP...........................

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selec

VMariaS [17]

Answer:

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

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".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 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)

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

$df=n-1=9-1=8$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that $t_{\alpha/2}=$

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

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

5 0

3 years ago

A semicircular archway is built in front of a garden using 8 congruent granite tiles, as shown in the diagram. Find the area of

crimeas [40]

So there's 8 tiles.
Radius from archway to the outer edge would be : 7 +1 = 8ft

You can use this formula to count the area of semi circle : π r^2/2

A = 3.14 x 8ft^2 = 100.48 ft ^2
A = 3.14 x 7ft^2= 76.92 ft^2

100.48 - 76.92 = 23.55 ft^2

Then you have to divide it with the total tiles
23.55/8 = 2.94 ft^2 per tile >> (rounded to nearest tenth)

hope this helps

5 0

3 years ago

I Need Help Like Now!!

kogti [31]

Answer:

$\frac{136}{999}$

Step-by-step explanation:

We require 2 equations with the repeating decimal after the decimal point in both equations.

The bar above 136 indicates that 136 is being repeated

let x = 0.136136...... → (1) Multiply both sides by 1000

1000x = 136.136.... → (2)

Subtract (1) from (2) to eliminate the decimal part

999x = 136 ( divide both sides by 999 )

x = $\frac{136}{999}$

5 0

3 years ago

If 1/2x+1/3=4 What is the value of 3x+2y

ivolga24 [154]

Answer:

x=3/22 ; y=-9/44

Step-by-step explanation:

1/2x+1/3=4

=>1/2x=4-1/3

=>1/2x=(12-1)/3

=>1/2x=11/3

=>22x=3

=>x=3/22....(1)

then,

3x+2y

2y=-3 . (3/22)

y=-9/44

6 0

3 years ago

Read 2 more answers

What's 235 divided by 40

Alik [6]

5.875 is the answer

4 0

3 years ago

Read 2 more answers