Multiple choice answers are clearly defined as below for clarity:
A. the average squared deviations about the mean of a distribution of values.
B. an empirically testable statement that is an unproven supposition developed in order to explain certain phenomena.
C. the error made by rejecting the null hypothesis when it is true.
D. a statement that asserts the status quo; that is, any change from what has been thought to be true is due to random sampling order.
E. a statement that is the opposite of the null hypothesis
Answer:
A. The average squared deviations about the mean of a distribution of values.
Explanation:
A. the average squared deviations about the mean of a distribution of values. Correct
Standard deviation is how data is distributed around the mean. It is also the square root of the Variance. Therefore, the variance is the square of the standard deviation which is distributed around the mean.
B. an empirically testable statement that is an unproven supposition developed in order to explain certain phenomena. Incorrect
This is false as this is rather the definition for hypothesis.
C. the error made by rejecting the null hypothesis when it is true. Incorrect
This is false as this is the definition for the probability of committing a type I error
D. a statement that asserts the status quo; that is, any change from what has been thought to be true is due to random sampling order. Incorrect
This is false as this defines what a null hypothesis is.
E. a statement that is the opposite of the null hypothesis. Incorrect
The opposite of the null hypothesis is alternative hypothesis.
![\bf 1050=1020\left[ 1+r\left( \frac{3}{2} \right) \right]\implies \cfrac{1050}{1020}=1+r\left( \frac{3}{2} \right) \implies \cfrac{35}{34}=1+r\left( \frac{3}{2} \right) \\\\\\ \cfrac{35}{34}-1=\cfrac{3}{2}r\implies \cfrac{1}{34}=\cfrac{3}{2}r\implies \cfrac{2\cdot 1}{3\cdot 34}=r\implies \cfrac{1}{51}=r \\\\\\ r\%=100\cdot \cfrac{1}{51}\implies r\approx\stackrel{\%}{1.96078431372549}](https://tex.z-dn.net/?f=%5Cbf%201050%3D1020%5Cleft%5B%201%2Br%5Cleft%28%20%5Cfrac%7B3%7D%7B2%7D%20%5Cright%29%20%5Cright%5D%5Cimplies%20%5Ccfrac%7B1050%7D%7B1020%7D%3D1%2Br%5Cleft%28%20%5Cfrac%7B3%7D%7B2%7D%20%5Cright%29%20%5Cimplies%20%5Ccfrac%7B35%7D%7B34%7D%3D1%2Br%5Cleft%28%20%5Cfrac%7B3%7D%7B2%7D%20%5Cright%29%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B35%7D%7B34%7D-1%3D%5Ccfrac%7B3%7D%7B2%7Dr%5Cimplies%20%5Ccfrac%7B1%7D%7B34%7D%3D%5Ccfrac%7B3%7D%7B2%7Dr%5Cimplies%20%5Ccfrac%7B2%5Ccdot%201%7D%7B3%5Ccdot%2034%7D%3Dr%5Cimplies%20%5Ccfrac%7B1%7D%7B51%7D%3Dr%0A%5C%5C%5C%5C%5C%5C%0Ar%5C%25%3D100%5Ccdot%20%5Ccfrac%7B1%7D%7B51%7D%5Cimplies%20r%5Capprox%5Cstackrel%7B%5C%25%7D%7B1.96078431372549%7D)
