Plot C(-1,–7), D (6,–7), E(5,3), and F(5,-5) in a coordinate plane. Are CD and EF congruent?
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Answer:
The 95% confidence interval would be given by
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".
represent the sample mean 1
represent the sample mean 2
n1=10 represent the sample 1 size
n2=10 represent the sample 2 size
sample standard deviation for sample 1
sample standard deviation for sample 2
represent the population standard deviation
parameter of interest.
Part a
The confidence interval for the difference of means is given by the following formula:
(1)
The point of estimate for is just given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that
The standard error is given by the following formula:
And replacing we have:
Confidence interval
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by
If the system of hypothesis are given by:
Null Hypothesis:
Alternative hypothesis:
The statistic would be:
And if we replace we got:
And the p value would be given by:
And with 5% of significance we have enough evidence to reject the null hypothesis since the