A shade of green paint is created by mixing a certain amount yellow paint with a certain amount of blue paint. The ratio of yell
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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 . 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 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:
represent the sample mean for the difference
population mean (variable of interest)
=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:
(1)
In order to calculate the critical value t we need to find first the degrees of freedom, given by:
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
Now we have everything in order to replace into formula (1):
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 . 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.
We sketch two triangles, DFE and DGH, as shown below
Side DF correspond to side DG, the scale factor is 40÷32=1.25
Side DE correspond to side DH, the scale factor is 30÷24=1.25
That leaves us with the last corresponding sides, EF and HG which would also have a scale factor 1.25
Both triangles share the same angle D
We can conclude triangle DFE and triangle DGH are similar for property SSS and SAS
Side DF correspond to side DG, the scale factor is 40÷32=1.25
Side DE correspond to side DH, the scale factor is 30÷24=1.25
That leaves us with the last corresponding sides, EF and HG which would also have a scale factor 1.25
Both triangles share the same angle D
We can conclude triangle DFE and triangle DGH are similar for property SSS and SAS