Use a t-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assume the results
1 answer:
Answer:
Step-by-step explanation:
Given that we can Assume the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d=x1-x2. Test H0 : μd=0 vs Ha : μd≠0
Here test statistic = Mean difference ./std error
= Mean difference/(std dev/(sqrt n))
=
df =24
p value = 0.000121
Since p < alpha, we reject null hypothesis.
The two means are significantly different.
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Answer:
Step-by-step explanation:
The formula for the dot product of vectors is
u·v = |u||v|cosθ
where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.
which is
which is
I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.
We also need the angle, which of course has its own formula.
where uv has ITS own formula:
uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.
uv = 96.
To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:
which returns an angle measure of 30.7. Plugging that all into the dot product formula:
gives you a dot product of 96