- if A and B ARE mutually exclusive then the events cannot occur at the same time
- Then there is no intersection
- Since they cannot both occur so in that case it's just P(A) + P(B)
**For**NON mutually exclusive events they can both occur at the same time**s**o we have an intersection of the events A and B, so we still have P(A) + P(B) but now see if we add A and B we are also adding the intersected part, so really adding a part of A and a Part of B twice so to just get A or B we have to remove that part, so subtract off P(A and B)

## Friday, March 31, 2017

## Monday, March 20, 2017

### hypothesis test for proportions, things to remember

Here's a few things to remember

Z scores for proportion

(p^ - p)/square root(p*(1-p)/n)

Z for difference of two proportion

(p1^ - p2^)/square root(p-bar(1-p-bar)/n1 + (p-bar(1-p-bar)/n2))

p-bar = (x1 +x2)/(n1 + n2)

Note that p-bar might also be noted at p-pooled

For hypotheses, remember that Ho always contains = and Ha contains <, > or "does not equal"

Confidence intervals for single proportion

p^ +/- Z*square root(p^(1-p^)/n)

For difference of two propotions

p1^ - p2^ +/- Z*square root(p1^(1-p1^)/n1 + p2^(1-p2^)/n2)

Z values for confidence intervals

90% = 1.645

95% = 1.96

98% = 2.33

99% = 2.575

You can also get these from Z chart

P-values are the value from the Z chart for corresponding Z score if Ha contains < and 1- value from the Z chart for corresponding Z score if Ha contains >. If Ha is "does not equal" you take 1 - value from the Z chart for corresponding Z score then multiply the result by 2.

You can also get p-values from Z scores using the link below.

http://www.socscistatistics.com/pvalues/normaldistribution.aspx

Z scores for proportion

(p^ - p)/square root(p*(1-p)/n)

Z for difference of two proportion

(p1^ - p2^)/square root(p-bar(1-p-bar)/n1 + (p-bar(1-p-bar)/n2))

p-bar = (x1 +x2)/(n1 + n2)

Note that p-bar might also be noted at p-pooled

For hypotheses, remember that Ho always contains = and Ha contains <, > or "does not equal"

Confidence intervals for single proportion

p^ +/- Z*square root(p^(1-p^)/n)

For difference of two propotions

p1^ - p2^ +/- Z*square root(p1^(1-p1^)/n1 + p2^(1-p2^)/n2)

Z values for confidence intervals

90% = 1.645

95% = 1.96

98% = 2.33

99% = 2.575

You can also get these from Z chart

P-values are the value from the Z chart for corresponding Z score if Ha contains < and 1- value from the Z chart for corresponding Z score if Ha contains >. If Ha is "does not equal" you take 1 - value from the Z chart for corresponding Z score then multiply the result by 2.

You can also get p-values from Z scores using the link below.

http://www.socscistatistics.com/pvalues/normaldistribution.aspx

## Monday, March 6, 2017

### Finding half life

Solving for the half life is easy.

Suppose A(t) = Ao*e^(-4t)

To find the half life, let A(t) = (1/2)Ao

(1/2)Ao = Ao*e^(-4t)

1/2 = e^(-4t)

ln (1/2) = ln(e^(-4t))

ln (1/2) = -4t

t = (-1/4)ln(1/2)

Suppose A(t) = Ao*e^(-4t)

To find the half life, let A(t) = (1/2)Ao

(1/2)Ao = Ao*e^(-4t)

1/2 = e^(-4t)

ln (1/2) = ln(e^(-4t))

ln (1/2) = -4t

t = (-1/4)ln(1/2)

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