Answer:
The least common denominator is 21
Step-by-step explanation:
3 & 7 equal 21 which is the least common factor that it equals
Answer:
141.291667 or about 141
Step-by-step explanation:
Check the picture below, so the circle looks more or less like so, with a radius of 9.
![\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies C=2\pi (9)\implies C\approx 57](https://tex.z-dn.net/?f=%5Ctextit%7Bcircumference%20of%20a%20circle%7D%5C%5C%5C%5C%20C%3D2%5Cpi%20r~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D9%20%5Cend%7Bcases%7D%5Cimplies%20C%3D2%5Cpi%20%289%29%5Cimplies%20C%5Capprox%2057)
We don't know what the exact p-value is, but we are told that it's as large as 0.005 which is smaller than alpha = 0.05
Since the p-value is smaller than alpha, this means we <u>reject the null hypothesis</u>.
The way you can remember this is "if the p-value is low, then the null must go". By "low", I mean "smaller than alpha".
Recall that the p-value is the probability of observing that specific test statistic, or larger. So the chances of chi-squared being 18.68 or larger is a probability between 0.0025 and 0.005; there's a very small chance of this happening. The p-value is based entirely on the assumption that the null is correct. But if the null is correct, then the chances of landing on this are very small. We have a contradiction that basically leads to us concluding the null must not be the case. It's not 100% guaranteed of course, but it's fairly strong evidence.
In short, the p-value being smaller than alpha = 0.05 means we reject the null.
In order to accept the null, the p-value must be 0.05 or larger.
Answer:
The probability is 1216 chance, which is approximately a 0.46% chance
