What is the mean absolute deviation of 10, 5, 7, 10, 19, 32, 25?

Consider the following hypothesis test: H0: LaTeX: \mu_1-\mu_2=0μ 1 − μ 2 = 0 Ha: LaTeX: \mu_1-\mu_2\ne0μ 1 − μ 2 ≠ 0 The follow

Pavel [41]

Answer:

$z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53$

Step-by-step explanation:

Data given and notation

$\bar X_{1}=104$ represent the mean for the sample 1

$\bar X_{2}=106$ represent the mean for the sample 2

$\sigma_{1} =8.4$ represent the population standard deviation for the sample 1

$\sigma_{2}=7.6$ represent the population standard deviation for the sample 2

$n_{1}=80$ sample size for the group 1

$n_{2}=70$ sample size for the group 2

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0: $\mu_{1}-\mu_{2} =0$

H1: $\mu_{1} -\mu_{2} \neq 0$

If we analyze the size for the samples both are greater than 30 and we know the population deviations so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:

And with this we can replace in formula (1) like this:

$z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53$

7 0

3 years ago

You know that a rope is no more than 150 feet long. You need to cut the rope into 3 pieces.

Sunny_sXe [5.5K]

Answer:

80 ft

Step-by-step explanation:

hey there,

< We know that the rope is 3 pieces long. To make this into an equation, let's just write x + y + z = 150.

Assuming "y" is our second piece, we can tell y = 2x, because it is two times the size of the first piece, which is "x". We also know "z" (our third piece): z = 30.

We can try inputting all the things we know now. x + (2x) + 30 = 150. From here, we can find that x = 40. Since y is our second piece, y = 2x, so 2 x (40) = 80. The second piece would be 80 feet long. >

Hope this helped! Feel free to ask anything else.

7 0

3 years ago

Is this answer correct?

BabaBlast [244]

Yes the mean is the middle number so go according to the order from smallest to biggest 48 is the middle number

5 0

3 years ago

Solve the following system. y = x 2 - 9x + 10 and x + y + 5 = 0. The solutions are

shepuryov [24]

X+y+5=0

y=-x-5

If a solution exists y=y so we can say

x^2-9x+10=-x-5 add x+5 to both sides

x^2-8x+15=0 now factor

x^2-3x-5x+15=0

x(x-3)-5(x-3)

(x-5)(x-3) so x=3 and 5, using y=-x-5

y(3)=-8 and y(5)=-10

So the two solutions are:

(3,-8) and (5,-10)

6 0

3 years ago

Read 2 more answers

Tamara is going to the laundromat. She needs 6 quarters for each of the 4 machines that she is using. How many dollar bills must

jekas [21]

6 x 4 = 24

24 / 4 (#ofquartersinadollar) = 6
It’s option D.

5 0

3 years ago

Read 2 more answers

What is the mean absolute deviation of 10, 5, 7, 10, 19, 32, 25?​

What is the mean absolute deviation of 10, 5, 7, 10, 19, 32, 25?