The mean of normally distributed test scores is 82 and the standard deviation is 5. If there are 241 test scores in the data sample, how many of them were in the 92 to 97 range?

Answer:

The  95% confidence interval is  [tex]0.449 < p < 0.48 + 0.511[/tex]

Step-by-step explanation:

From the question we are told that  

     The sample proportion is [tex]\r p = 0.48[/tex]

      The sample size is [tex]n = 1022[/tex]

Given that the confidence level is 95%  then the level of significance is mathematically evaluated as

       [tex]\alpha = 100 - 95[/tex]

       [tex]\alpha = 5 \%[/tex]

       [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is

     [tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }= 1.96[/tex]

The reason we are obtaining critical value of    [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because  

 [tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval (   [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while     [tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

    Generally the margin of error is mathematically represented as

         [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p )}{n} }[/tex]

substituting values

          [tex]E = 1.96* \sqrt{\frac{0.48 (1- 0.48 )}{1022} }[/tex]

          [tex]E = 0.03063[/tex]

The 95% confidence interval is mathematically represented as

      [tex]\r p - E < p < \r p + E[/tex]

substituting values

       [tex]0.48 - 0.03063 < p < 0.48 + 0.03063[/tex]

       [tex]0.449 < p < 0.48 + 0.511[/tex]

Answer:

- 29 / 20

Step-by-step explanation

The cosec (x) = 1 / sin(x)

There are 2 ways to do this:

Either using a calculator:

sin^-1(20 / 29) = 43.60281897

so inputting into 1/sin(-x) where x = 43.6.....

This gives: -29 / 20

OR

1 / sin(x) = cosec ( x)

so cosec (x) = 1/(20/29)

= 29/20

By observing the cosec(x) graph, we see that to get cosec (-x), all we need to do is to minus our answer seeing as the graph is symmetrical across the axes. Therefore x = -29/20

One number = x

One number more 26 = x + 26

Their product is -169

x . (x + 26) = -169

x² + 26x = -169

x² + 26x + 169 = 0

x² + 2.13.x + 13² = 0

It can be written by

(x + 13)² since we know that (x + 13)² = x² + 2.x.13 + 13²

So

(x + 13)² = 0

x + 13 = 0

x = -13

Our number is -13

Step-by-step explanation:

Here, according to the question,

let one number be x and another number be x +26 as given in question that the another number is more than 26.

And their product is given as -169.

now, as per the condition of question,

x × (x+26)= -169

or, x^2+26x= -169

or, x^2+26x+169=0

or, (x+13)^2=0

or, (x+13)=0 (root under 0= 0)

or, x=-13.

Therefore, thevalue of x is -13.

And the value of (x+26) is (-13+26)=13.

Checking, 13×-13=-169.

Therefore, the 2 numbers are -13 and 13.

hope it helps...

Answer:

Step-by-step explanation:

lot = 120 face shields

sold 5/6 of 120 =

5 × 120 ÷ 6 =

600 ÷ 6 = 100 sold of the lot.

then: 120-100 = 20

They need to sell 20 protectors.

Answer:

20 face shields.

Step-by-step explanation:

You have 120 face shields.

You sell 5/6 of them. That means that you still have to sell 1 - 5/6 = 1/6 of the lot.

120 * (1/6) = 20 * 1 = 20 face shields to sell.

Hope this helps!

Answer:

Step-by-step explanation:

To find Angle B we use sine

sin∅ = opposite / hypotenuse

From the question

AB is the hypotenuse

AC is the opposite

So we have

sin B = AC / AB

sin B = 4/9

B = sin-¹ 4/9

B = 26.38

B = 26° to the nearest hundredth

Hope this helps you

Answer:

[tex]\boxed{ \sf 26.39}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions.

[tex]\sf sin(\theta )=\frac{opposite}{hypotenuse}[/tex]

[tex]\sf sin(?)=\frac{4}{9}[/tex]

[tex]\sf ?=sin^{-1}(\frac{4}{9} )[/tex]

[tex]\sf ? =26.38779996...[/tex]

Answer:

34.49 m

Step-by-step explanation:

Use the formula height = [tex]\frac{v^{2} }{2g}[/tex]

1. Substitute in the values given

26² / 2(9.8)

2. Simplify and solve

676 / 19.6 = 34.49

Answer:

The answer is C: 34 m

Answer:

centre = (13,0)

radius = 8

Step-by-step explanation:

The standard equation of the circle is

(x-x0)^2 + (y-y0)^2 = r^2 ...............(1)

where

(x0,y0) is the centre,

r is the radius.

For

(x-13)^2 + y^2 = 64  ..............(2)

we rewrite (2)

(x-13)^2 + (y-0)^2 = 8^2 ...............(3)

and compare (3) with (1)

to identify

x0 = 13, y0 = 0, and r = 8

Therefore

centre = (13,0)

radius = 8

First,

[tex]9x+15y+15z=45\implies 3x+5y+5z=15[/tex]

The volume is given by the integral (one of 6 possible combinations),

[tex]\displaystyle\int_0^5\int_0^{\frac{15-3x}5}\int_0^{\frac{15-3x-5y}5}\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{\frac{15}2}[/tex]

Answer:

The answer is A.

Step-by-step explanation:

You have to multiply by converting the second fraction into upside down :

[tex] \frac{4x + 1}{6x} \div \frac{x}{3x - 1} [/tex]

[tex] = \frac{4x + 1}{6x} \times \frac{3x - 1}{x} [/tex]

[tex] = \frac{(4x + 1)(3x - 1)}{x(6x)} [/tex]

[tex] = \frac{12 {x}^{2} - 4x + 3x - 1}{6 {x}^{2} } [/tex]

[tex] = \frac{12 {x}^{2} - x - 1 }{6 {x}^{2} } [/tex]

Answer:

Step-by-step explanation:

The mean which is also known as the average is determined by dividing the sum of the weight of the packages by the total number of packages. From the information given,

Mean = (26 + 18 + 58 + 22 + 54 + 50)/6 = 38

If you include a package that weighs 66 ounces, the new mean would be

New mean = (26 + 18 + 58 + 22 + 54 + 50 + 66)/7 = 42

For the median, we would rearrange the weights in ascending order. It becomes

18, 22, 26, 50, 54, 58

Median = (26 + 50)/2 = 38

By adding the new weight, it becomes

18, 22, 26, 50, 54, 58, 66

New median = 50

It can be seen that both the median increased by more. It increased by 12 while the mean increased by 4

Answer: The mean which is also known as the average is determined by dividing the sum of the weight of the packages by the total number of packages. From the information given, Mean = (26 + 18 + 58 + 22 + 54 + 50)/6 = 38If you include a package that weighs 66 ounces, the new mean would be New mean = (26 + 18 + 58 + 22 + 54 + 50 + 66)/7 = 42For the median, we would rearrange the weights in ascending order. It becomes18, 22, 26, 50, 54, 58Median = (26 + 50)/2 = 38By adding the new weight, it becomes18, 22, 26, 50, 54, 58, 66New median = 50It can be seen that both the median increased by more. It increased by 12 while the mean increased by 4

Step-by-step explanation:

Answer:

it is A!! hope this helped mark brainly

Answer:

21

Step-by-step explanation:

Just like a dilation you want to find some sort of scale factor. Now when 7/2 is simplified it then becomes 3.5. Now multiply that by 6 since we are trying to find the ratio. when multiplied by 6 it becomes 21 so the ration of wins to losses is 21/6

Answer:

15.625 m³

Step-by-step explanation:

The volume of a cube has a formula: V = a³

V = volume

a = side length

The side length is given 2.5 meters.

V = 2.5³

Solve for V.

V = 15.625

The volume is 15.625 cubic meters.

Answer:

15.625cm^3

Step-by-step explanation:

Formula:

V=lxwxh

Given:

l=2.5m

w=2.5m

h=2.5m

Answer:

V=lxwxh

V=2.5m*2.5m*2.5m

V=6.25m^2*2.5m

V=15.625m^3

Hope this helps :)

Answer:

k = 44

Step-by-step explanation:

k/4 + 3 = 14

k/4 = 11

k = 44

Answer:

[tex]\boxed{\sf k=44}[/tex]

Step-by-step explanation:

[tex]\sf \frac{k}{4} +3=14[/tex]

Subtract 3 from both sides.

[tex]\sf \frac{k}{4} +3-3=14-3[/tex]

[tex]\sf \frac{k}{4}=11[/tex]

Multiply both sides by 4.

[tex]\sf \frac{k}{4}(4)=11(4)[/tex]

[tex]\sf k=44[/tex]

Answer:

$7

Step-by-step explanation:

Simple interest formula:

I = Prt

6 months = 6 * 30 days = 180 days

1 year = 360 days

t = (180 days)/(360 days) = 0.5

I = $7000 * 0.002 * 0.5

I = $7

Answer:

$7

Step-by-step explanation:

Recall that simple interest is given by

I = Prt,

Where :

I = interest (we are asked to find this)

P = principal amount = given as $7000

r = rate = given as 0.2% = 0.002

t = time in years = given as 6 months = 0.5 years

SImply substitute the known values into the equation above:

I = Prt

= (7000)(0.002)(0.5)

= $7

Answer:

The first option.

Step-by-step explanation:

y-intercept equation: y=mx+b

mx=slope

b=y-intercept

Looking at the graph, we can know that the slope is 1/3x so we can eliminate the 2nd choice. Now, we fix the second inequality into the y-intercept form which is

1st option: y>3x-2

3rd option: y>-3x+2

4th option: y>2x-2

Now, looking at the blue graph, the slope is 3x. And looking at the y-intercept,  it is on -2.

So, it will be the first option!

Hope this helps, and BRAINLIEST would help me a lot!

Answer:

[tex]y=\frac{4}{3}x-1.75[/tex]

Step-by-step explanation:

If the slope of a line is 4/3,

and we wanna find the equation of a line that is parallel to it and crosses through (5,5).

So we already have the slope because the slope of 2 parallel lines are the same.

y = 4/3x

Look at the image below↓

So now we just need to find the y-intercept.

After some numbers we got,

[tex]y=\frac{4}{3}x-1.75[/tex]

Look at the other image below↓

Thus,

the equation of the parallel line is [tex]y=\frac{4}{3}x-1.75[/tex].

Hope this helps :)

Answer:

Following are the answer to this question:

Step-by-step explanation:

The principle vale of Arg(3)

[tex]Arg(3)=-\pi+\tan^{-1} (\frac{|Y|}{|x|})[/tex]

The principle value of the [tex]\logi= \log(0+i)\ \ \ \ \ _{where} \ \ \ x=0 \ \ y=1> 0[/tex]

So, the principle value:

a)

[tex]\to \log(i)=\log |i|+i Arg(i)\\\\[/tex]

             [tex]=\log \sqrt{0+1}+i \tan^{-1}(\frac{1}{0})\\\=\log 1 +i \tan^{-1}(\infty)\\\=0+i\frac{\pi}{2}\\\=i\frac{\pi}{2}[/tex]

b)

[tex]\to \log(-i)= \log(0-i ) \ \ \ x=0 \ \ \ y= -1<0\\[/tex]

Principle value:

[tex]\to \log(-i)= \log|-i|+iArg(-i) \\\\[/tex]

                 [tex]=\log \sqrt{0+1}+i(-\pi+\tan^{-1}(\infty))\\\\=\log1 + i(-\pi+\frac{\pi}{2})\\\\=-i\frac{\pi}{2}[/tex]

c)

[tex]\to \log(-1+i) \ \ \ \ x=-1, _{and} y=1 \ \ \ x<0 and y>0[/tex]

The principle value:

[tex]\to \log(-1+i)=\log |-1+i| + i Arg(-1+i)[/tex]

                     [tex]=\log \sqrt{1+1}+i(\pi+\tan^{-1}(\frac{1}{1}))\\\\=\log \sqrt{2} + i(\pi-\tan^{-1}\frac{\pi}{4})\\\\=\log \sqrt{2} + i\tan^{-1}\frac{3\pi}{4}\\\\[/tex]

d)

[tex]\to i^i=w\\\\w=e^{i\log i}[/tex]

The principle value:

[tex]\to \log i=i\frac{\pi}{2}\\\\\to w=e^{i(i \frac{\pi}{2})}\\\\=e^{-\frac{\pi}{2}}[/tex]

e)

[tex]\to (-i)^i\\\to w=(-i)^i\\\\w=e^{i \log (-i)}[/tex]

In this we calculate the principle value from b:

so, the final value is [tex]e^{\frac{\pi}{2}}[/tex]

f)

[tex]\to -1^i\\\\\to w=e^{i log(-1)}\\\\\ principle \ value: \\\\\to \log(-1)= \log |-1|+iArg(-i)[/tex]

                [tex]=\log \sqrt{1} + i(\pi-\tan^{-1}\frac{0}{-1})\\\\=\log \sqrt{1} + i(\pi-0)\\\\=\log \sqrt{1} + i\pi\\\\=0+i\pi\\=i\pi[/tex]

and the principle value of w is = [tex]e^{\pi}[/tex]

g)

[tex]\to -1^{-i}\\\\\to w=e^(-i \log (-1))\\\\[/tex]

from the point f the principle value is:

[tex]\to \log(-1)= i\pi\\\to w= e^{-i(i\pi)}\\\\\to w=e^{\pi}[/tex]

h)

[tex]\to \log(-1-i)\\\\\ Here x=-1 ,<0 \ \ y=-1<0\\\\ \ principle \ value \ is:\\\\ \to \log(-1-i)=\log\sqrt{1+1}+i(-\pi+\tan^{-1}(1))[/tex]

                    [tex]=\log\sqrt{2}+i(-\pi+\frac{\pi}{4})\\\\=\log\sqrt{2}+i(-\frac{3\pi}{4})\\\\=\log\sqrt{2}-i\frac{3\pi}{4})\\[/tex]

Answer:

Step-by-step explanation:

Probability is defines as the likelihood or chance that an event will occur.

Probability = expected outcome of event/total outcome.

Since a single die with 9 sides was rolled, the total event outcome will be 9*9 = 81

Expected outcome will be the event that the sum of the two rolls equals 3. The possible outcomes are {(1,2), (2,1)}. The expected outcome is 2

Probability that the sum of the two rolls equals 3 = 2/81

The probability that the sum of the two rolls equals 3 is [tex]\dfrac{2}{81}[/tex].

Important information:

We need to find the probability that the sum of the two rolls equals 3.

If a die with 9 sides is rolled twice, then the number of total possible outcomes is:

[tex]9\times 9=81[/tex]

The sum of the two rolls equals 3, if we get 1, 2 and 2, 1. It means the number of favorable outcomes is 2.

[tex]P=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]P=\dfrac{2}{81}[/tex]

Therefore, the probability that the sum of the two rolls equals 3 is [tex]\dfrac{2}{81}[/tex].

Find out more about 'Probability' here:

https://brainly.com/question/6778390

Answer:

Step-by-step explanation:

This problem is on the mensuration of solids, a cylinder and a cone combined (a frustum)

We are required to solve for the total curve surface areas both solids

hence the curve surface area (henceforth CSA) of a cylinder is given as

[tex]CSA-cylinder=2\pi rh[/tex]

[tex]CSA-cone= \pi rl[/tex]

[tex]Total CSA= 2\pi rh+\pi rl[/tex]

Given data

diameter d= 20

radius = d/2= 20/2= 10

height of cylinder h= 9

slant height of cone l= 16

substituting our data into the expression we have

[tex]Total -CSA= 2*\pi *10*9+\pi *10*16\\\\Total -CSA= 565.56+502.72\\\Total -CSA= 1068.28[/tex]

Answer:

C. 0.0009

Step-by-step explanation:

0.09/100

= 0.0009

Answer:A

Step-by-step explanation:0.09=0.9

Answer: 2neters

Step-by-step explanation: I also recently did it on Khan academy

The height of the tent of the figure is H = 2 m

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

Let the volume of the tent be represented as V

Now , the value of V is

V = 4.5 m³

Let the height of the prism be H

Now , the base of the triangle B = 1.5 m

And , the length of the tent L = 3 m

So , Volume of Prism = B x h

4.5 = ( 1/2 ) x 1.5 x H x 3

On simplifying , we get

4.5 = 2.25H

Divide by 2.25 on both sides , we get

H = 2 m

Hence , the height of the tent is 2 m

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The complete question is attached below :

Syrus is buying a tent with the dimensions shown below. The volume inside the tent is 4.5 m^3. Syrus isn't sure if the tent will be tall enough for him to stand inside. What is the height of the tent?

Answer:

Reject H0

Age and pressure are related

Step-by-step explanation:

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.

Answer:

a=6

b=5.5

Step-by-step explanation:

not very sure but..

since 8X2=16,

a=3X2

b=11/2

Answer:  3/(28) ≈ 10.7%

Step-by-step explanation:

3 blue + 2 red + 3 green = 8 total pens

   First pick    and           Second pick

 [tex]\dfrac{3\ blue\ pens}{8\ total\ pens}\quad \times \quad \dfrac{2\ remaining\ blue\ pens}{7\ remaining\ total\ pens}\quad =\large\boxed{\dfrac{3}{28}}[/tex]  

Answer:

3

Step-by-step explanation:

Because the number 5 is a number that you get from 7 more than n, and 2 is the other divisor that means n must equal 10 and 7 less than 10 is 3.

When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.

Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable).

In the question, we are asked to find a number, which satisfies the statement, "Five times a number is divided by 7 more than the number. The result of this division is 2".

We assume the number to be x.

Now we try to form a linear equation in one variable from the given statement.

Five times a number is 5x.

7 more than a number is x + 7.

We are said that five times a number is divided by 7 more than a number. This can be shown as 5x/(x + 7).

Now, the result is given as 2, which can be shown as:

5x/(x+ 7) = 2, which is the required linear equation in one variable.

To get the number, we solve the equation using the following steps:

5x/(x+ 7) = 2

or, {5x/(x+ 7)}*(x + 7) = 2*(x + 7) (Multiplying both sides by (x + 7))

or, 5x = 2x + 14 (Simplifying)

or, 5x - 2x = 2x + 14 - 2x (Subtracting 2x from both sides)

or, 3x = 14 (Simplifying)

or, 3x/3 = 14/3 (Dividing both sides by 3)

or, x = 14/3 (Simplifying)

∴ When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.

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Answer:

x=4

Step-by-step explanation:

3/4x+ 4 = 7

Subtract 4 from each side

3/4x+ 4-4 = 7-4

3/4x = 3

Multiply each side by 4/3

4/3 * 3/4 x = 3 * 4/3

x = 4

Answer:

Largest possible length is 21 inches.

Step-by-step explanation:

Given:

Total material available = 60 inches

Length to be 3 more than twice of width.

To find:

Largest possible length = ?

Solution:

As it is rectangular shaped frame.

Let length = [tex]l[/tex] inches and

Width = [tex]w[/tex] inches

As per given condition:

[tex]l = 2w+3[/tex] ..... (1)

Total frame available = 60 inches.

i.e. it will be the perimeter of the rectangle.

Formula for perimeter of rectangle is given as:

[tex]P = 2 \times (Width + Length)[/tex]

Putting the given values and conditions as per equation (1):

[tex]60 = 2 \times (w+ l)\\\Rightarrow 60 = 2 \times (w+ 2w+3)\\\Rightarrow 60 = 2 \times (3w+3)\\\Rightarrow 30 = 3w+3\\\Rightarrow 3w = 27\\\Rightarrow w = 9 \ inch[/tex]

Putting in equation (1):

[tex]l = 2\times 9+3\\\Rightarrow l = 21\ inch[/tex]

So, the answer is:

Largest possible length is 21 inches.

Answer:

Probability that at least two of them would survive another five years = 0.388

Step-by-step explanation:

We are given;

Probability of Survival of 60 years old for the next 5 years;

P(60 years old surviving) = 0.7  

Thus;

Probability of 60 years old not surviving for the next 5 years;

P(60 years old not surviving) = 1 - 0.7  = 0.3

Also,given;

Probability of Survival of 65 years old for the next 5 years;

P(65 years old surviving)  =  0.4  

Thus;

Probability of 65 years old not surviving for the next 5 years;

P(65 years not surviving)  =  1 - 0.4  = 0.6

Also,given;

Probability of Survival of 70 years old for the next 5 years;

P(70 years old surviving)  =  0.2  

Thus;

Probability of 70 years old not surviving for the next 5 years;

P(70 years not surviving)  =  1 - 0.2   = 0.8

Probability that at least two survived is;

P(at least 2 surviving) = [P(60 surviving) x P(65 surviving) x P(70 not surviving)] + [P(60 surviving) x P(65 not surviving) x P(70 surviving)] + [P(60 not surviving) x P(65 surviving) x P(70 surviving)] + [P(60 surviving) x P(65 surviving) x P(70 surviving)]

P(at least 2 surviving) = [(0.7)(0.4)(0.8)] + [(0.7)(0.6)(0.2)] + (0.3)(0.4)(0.2)  + [(0.7)(0.4)(0.2)]

P(at least 2 surviving) = 0.224  + 0.084  + 0.024 + 0.056

P(at least 2 surviving) = 0.388

Answer:

For 0,90 of Confidence we reject H₀

For  0,95 CI we reject H₀

Step-by-step explanation:

To evaluate a difference between two proportion with big sample sizes we proceed as follows

1.-Proportion 1

n = 2160

243 had rear license  p₁ = 243/2160     p₁ = 0,1125

2.Proportion 2

n = 358

55   had rear license   p₂ = 55/ 358     p₂ = 0,1536

Test Hypothesis

Null Hypothesis                            H₀      ⇒   p₂   =  p₁

Alternative Hypothesis                Hₐ     ⇒    p₂  >  p₁

With signficance level  of  0,05  means  z(c) = 1,64

T calculate   z(s)

z(s) =  ( p₂ - p₁ ) / √ p*q ( 1/n₁  +  1/n₂ )

p = ( x₁  +  x₂ ) / n₁  +  n₂

p = 243  +  55 / 2160 + 358

p = 0,1183     and then    q = 1 -  p     q =  0,8817

z(s) =  ( 0,1536 - 0,1125 ) / √ 0,1043 ( 1/ 2160   +  1 / 358)

z(s) =  0,0411 /√ 0,1043*0,003256

z(s) = 0,0411 / 0,01843

z(s) =  2,23

Then  z(s) > z(c)      2,23  >  1,64

z(s) is in the rejection region we reject H₀

If we construct a CI for  0,95   α = 0,05   α/2  =  0,025

z (score ) is  from z- table    z = 1,96

CI = ( p ±  z(0,025*SE)

CI = ( 0,1536 ± 1,96*√ 0,1043*0,003256 )

CI = ( 0,1536 ± 1.96*0,01843)

CI = ( 0,1536 ± 0,03612 )

CI = ( 0,11748  ;  0,18972 )

In the new CI we don´t find  0 value so we have enough evidence to reject H₀