Which of the following statements are true concerning the mean of the differences between two dependent samples (matched pairs)
1 answer:
Answer:
A and C
Step-by-step explanation:
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations we can use it.
And in order to conduct it we need to have some assumptions:
1) The dependent variable must be continuous (interval/ratio).
2) The observations are independent of one another.
3) The dependent variable should be approximately normally distributed.
4) The dependent variable should not contain any outliers.
Let's analyze one by one the options on this case:
A. The methods used to evaluate the mean of the differences between two dependent variables apply if one has 86 IQ scores of taxpayers from Texas and 86 IQ scores of taxpayers from Ohio
We can assume that is true since the two variables are dependent and we are assuming that all the other conditions are satisfied to use the t paired test.
B. The requirement of a simple random sample is satisfied if we have matched pairs of voluntary response data.
That's not neccesary true since is not a requirement in order to use the t pairedtest.
C. If one has more than 23 matched pairs of sample data, one can consider the sample to be large and there is no need to check for normality.
We can assume that is true since we need to ensure normality in order to apply the test and if the sample size is large enough large we can apply the test.
D. If one has twenty matched pairs of sample data, there is a loose requirement that the twenty differences appear to be from a normally distributed population.
False the requirement of normality is important to apply the test not a loose requirement.
E. If one wants to use a confidence interval to test the claim that mu Subscript d Baseline greater than 0 with a 0.01 significance level, the confidence interval should have a confidence level of 98%.
That's not correct the significance level is and that not correspond to the significance level given on this case.
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Answer:
Lots of connections!
Step-by-step explanation:
I attached some images to make it more clear.
Visual and verbal discussion:
A good starting point is the circle. One can think of a circle as the set of points that are equidistant to a certain point. In that sense, one can define a circle using the distance. At the same time, given a point in the plane, we can connect the point with the origin of the coordinates system forming a rectangle triangle! (See 2nd image)
Algebraic discussion:
1. The distance Formula:
Given two points in the plane and
we can find the distance between both points with the distance formula:
2. Equation of a circle centered at a point
3. The Pythagorean Theorem:
Given a triangle of sides and hypotenuse
we have that
Only by writing this equations we can already see the similarities between all three.
In fact, the most amazing thing about all three is that they are equivalents. That is, we can obtain every single one of them as an immediate result of another.
For instance, as I said before, one can think of a circle as the set of points equidistant to a certain origin or center point. So we could use the distance formula for each point on the circumference and we would obtain always the same value hence obtaining the equation of a circle.
Also as we discussed, any point on the plane form a rectangle triangle with its coordinates and calculating the distance of said point to the origin of the coordinate system would give us no other thing than the hypotenuse of said triangle!
