A value to describe the steepness of a straight line

In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean

Nastasia [14]

Answer:

a) $\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

b) $ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

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

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n=80 represent the sample size

Solution to the problem

Part a

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

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

For this case we can calculate the mean like this:

$\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

Part b

For this case is the sample size is doubled the margin of error would be:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

5 0

3 years ago

In order to make a specific shade of green paint, a painter mixes 1 1/2 quarts of blue paint, 2 cups of green paint, and 1/2 gal

ella [17]

Answer:

Step-by-step explanation:

In order to make a specific shade of green paint, a painter mixes 1 1/2 quarts of blue paint. Converting 1.5 quarts to cup,

1 quart = 4 cups

1.5 quarts = 1.5 × 4 = 6 cups

She also used 1/2 gallon of white paint. Converting 0.5 gallons to cup,

0.0625 gallons = 1 cup

0.5 gallons = 0.5/0.0625 = 8 cups

This means that the ratio of cups of blue paint to green paint to white paint is 6: 2 :8

Total ratio = 6 +2 + 8 = 16

To make 100 cups of this shade of green,

Cups of blue paint needed = 6/16 × 100 = 37.5 cups

Cups of green paint needed = 2/16 × 100 = 12.5 cups

Cups of white paint needed = 8/16 × 100 = 50 cups

7 0

3 years ago

A pair of jeans costs $40 and sales tax is 5%?<br>how much is the total bill?

spin [16.1K]

42$ because 10 % is 4 dollars so that 5% cut that 4 in half witch made it 2

5 0

3 years ago

Read 2 more answers

Can someone explain to me how to do this

rusak2 [61]

rank | 1st | 2nd |TOTAL
------|-----+-------|----------
a | 6 +    9 | =15
b | 7 + 3    | =16
c | 9 + 7    | =23
d | 6 + 7    | =22
e | 8 + 1 | =?

If you add the 1st in line a (6) and you add it to the 1st in line b (7) + the 2nd in line b (3) you get 16. Repeat the same logic/pattern to all c,d..
This is the pattern to all this puzzle;

So the before last term is : 9+6+7 = 22
and the last term : 6+8+1 = 15

7 0

3 years ago

Write an addition problem that has 9/10 as the sum

kicyunya [14]

There are a number of different problems that you could do that will give you an outcome of 9/10
For example, 1/2 and 2/5 add up to 9/10.
3/10 and 6/10 also add up to 9/10.

Find the sum of 7/10 and 1/5
Find the sum of 7/20 and 11/20
Find the sum of 1/2 and 3/10 and 1/10
Find the sum of 1/5 and 2/5 and 3/10

Hope this helps :)

3 0

3 years ago