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3 years ago

Help!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

2 answers:

Savatey [412]3 years ago

6 0

Diameter is 9 inch so the radius is 9/2=4.5inch
Part A: 2πr=28.26inch
π=28.26/(2r)
π=28.26/(2*4.5)=3.14
Part B: πr^2=63.585inch
π=63.585inch/(4.5inch)^2
π=3.139753086
Part C: Both of the answers are correct but Part B is more percise because it has more significant figures.

mixas84 [53]3 years ago

6 0

<h2>diameter is 9 inch so the radius is 9/2=4.5inch Part A: 2πr=28.26inch π=28.26/(2r) π=28.26/(2*4.5)=3.14 Part B: πr^2=63.585inchπ=63.585inch/(4.5inch)^2 π=3.139753086 Part C: Both of the answers are correct but Part B is more percise because it has more significant figures.</h2>

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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 $t_(\alpha/2)=2.306$