Question

If n=50, Std Dev from the mean =2, Tail = 1, what is P and how is it found? What if it is two tailed?

Inversely,

if n = 100, Std Dev from the mean is unknown, tails = 1, and P =.05, what is Std Dev and how is it found? What if it is two tailed?

Answer 1

1)

one tailed

p value = P(Z>2) = 0.0228   

excel formula for probability from z score is =NORMSDIST(-2)
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if two tailed,

p value = 2*P(Z>2) = 2 * 0.0228 = 0.0455

2)

one tailed

Z value at    0.05   =   -1.645   (excel formula =NORMSINV(   0.05   ) )
so, Std Dev from the mean = -1.645

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two tailed

p value = 0.05

z value at 0.05/2 = 0.025   = ±   1.960   (excel formula =NORMSINV(   0.05   / 2 ) )  
std dev from mean = 1.96