Which classification describes the system of linear equations?

A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain sca

saul85 [17]

Answer:

The 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between $-1.776 \leq \mu_d \leq 0.376$ . Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

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".

Let put some notation

x=test value before , y = test value after

x: 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8

y: 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7

The differences defined as $d_i = y_i -x_i$ and we got:

d: 0.3, -0.2, -0.3, -2.4, -3.1, 0.6, -0.4, -0.1

We can calculate the mean and the deviation for the sample with the following formulas:

$\bar d=\frac{\sum_{i=1}^n d_i}{n}$

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}$

$\bar d=-0.7$ represent the sample mean for the difference

$\mu_d$ population mean (variable of interest)

$s_d$ =1.32 represent the sample standard deviation

n=8 represent the sample size

Confidence interval

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

$\bar d \pm t_{\alpha/2} *\frac{s_d}{\sqrt{n}}$ (1)

In order to calculate the critical value t we need to find first the degrees of freedom, given by:

$df=n-1=8-1=7$

Since the Confidence is 0.95 or 95%, the value of alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that $t_(\alpha/2)=2.306$

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

$-0.7-2.306\frac{1.32}{\sqrt{8}}=-1.776$

$-0.7+2.306\frac{1.32}{\sqrt{8}}=0.376$

So on this case the 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between $-1.776 \leq \mu_d \leq 0.376$ . Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

6 0

3 years ago

Plz help the ones with question marks

3241004551 [841]

Answer:

1(5/16)=1.3125

7(5/16)=7.3125

26(5/16)=26.3125

Step-by-step explanation:

Given that 5/16=0.3125, the mixed fraction 1(5/16)=1+(5/16)=1+0.3125=1.3125

Also, 7(5/16)=7+(5/16)=7+0.3125=7.3125

Furthermore,

26(5/16)=26+(5/16)=26+0.3125=26.3125

In the same vein, given that 4/15=0.266

1(4/15)=1+(4/15)=1+0.266=1.266

17(4/15)=17+(4/15)=17+0.266=17.266

23(4/15)=23+(4/15)=23+0.266=23.266

7 0

2 years ago

Thanks for the help...........

Natali [406]

Answer:

Option C

Step-by-step explanation:

It was rotated to the right

6 0

3 years ago

In the diagram below, which distances would need to be the same in order for point A to be on the bisector of angle W? Explain w

Pachacha [2.7K]

Answer:

PA = XA

Step-by-step explanation:

Construction of an angle bisector,

1). Mark an arc from point W with the help of a compass which intersect lines WS and WZ at the points P and X respectively.

2). Marc two arcs of the same length form the points P and X which intersect each other at a point A.

3). Joint the points A and W.

Thus AW will be the angle bisector of angle PWX where PA = XA.

Therefore, distances PA and XA will be equal in measure.

4 0

3 years ago

The difference of two numbers is equal to 0.6. Their quotient is also 0.6. What are the numbers?

sveticcg [70]

Let one number be x and the other number be y.

The 2 equations are:
x - y = 0.6 --------------- (1)
x/y = 0.6 --------------- (2)

From equation (1):
x - y = 0.6
x = 0.6 + y --------------- Sub into (2)

$\dfrac{0.6 + y}{y} = 0.6$

0.6 + y= 0.6y

y - 0.6y = - 0.6

0.4y = - 0.6

y = -0.6 ÷ 0.4

y = -1.5

Sub y = -1.5 into (1):

x - y = 0.6

x - (-1.5) = 0.6

x + 1.5 = 0.6

x = 0.6 - 1.5

x = - 0.9

Answer: The numbers are -0.9 and -1.5

5 0

3 years ago