Since January Pohnpei has been experiencing sunnier, drier than normal weather due to a mild El Niño event. Pohnpei is naturally a rainy place. The rains of summer seem to be returning to the island during this past week. With that in mind the test tackles some rainy day statistics. The average number of days with rain per month is 21.7 days with a standard deviation of 2.7 days. The distribution of the number of days with rain per month is normally distributed.
Statistic or Parameter | Symbol | Equations | Excel |
---|---|---|---|
Normal Statistics | |||
Calculate a z value from an x | z | = | =STANDARDIZE(x, µ, s) |
Calculate an x value from a z | x | = s z + µ | =s*z+µ |
Calculate a z-statistic from an x | z | =(x - µ)/(sx/SQRT(n)) | |
Calculate a t-statistic (t-stat) | t | =(x - µ)/(sx/SQRT(n)) | |
Calculate an x from a z | =µ + zc*sx/sqrt(n) | ||
Find a probability p from a z value | =NORMSDIST(z) | ||
Find a z value from a probability p | =NORMSINV(p) | ||
Confidence interval statistics | |||
Degrees of freedom | df | = n-1 | =COUNT(data)-1 |
Find a zc value from a confidence level c | zc | =ABS(NORMSINV((1-c)/2)) | |
Find a tc value from a confidence level c | tc | =TINV(1-c,df) | |
Calculate an error tolerance E of a mean for n >= 30 using sx | E | =zc*sx/SQRT(n) | |
Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n >= 30. | E | =tc*sx/SQRT(n) | |
Calculate a confidence interval for a population mean µ from a sample mean x and an error tolerance E | x-E<= µ <=x+E |