For a sample size of n = 13 years (1971 to 1983 inclusive) the sample mean number of suicides in Chuuk state was = 9.92 suicides per year with a sample standard deviation of sx = 5.09 suicides per year. Construct a 95% confidence interval for the population mean m number of suicides per year in Chuuk State.
Statistic or Parameter | Symbol | Equations | Excel |
---|---|---|---|
Basic Statistics | |||
Square root | Ö | =SQRT(number) | |
Sample size | n | =COUNT(data) | |
Sample mean | Sx/n | =AVERAGE(data) | |
Sample standard deviation | sx | =STDEV(data) | |
Normal Statistics | |||
Calculate a z value from an x | z | ^{= } | =STANDARDIZE(x, m, s) |
Calculate an x value from a z | x | = s z + m | = s*z+m |
Calculate a z value from an | z | ||
Calculate an from a z | =m + z_{c}*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 | |
Find a z_{c} value from a confidence level c | z_{c} | =ABS(NORMSINV((1-c)/2)) | |
Find a t_{c} value from a confidence level c | t_{c} | =TINV(1-c,df) | |
Calculate an error tolerance E of a mean for n ³ 30 using sx | E | =z_{c}*sx/SQRT(n) | |
Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n ³ 30. | E | =t_{c}*sx/SQRT(n) | |
Calculate a confidence interval for a population mean m from a sample mean and an error tolerance E | -E< m <+E | ||
Hypothesis Testing | |||
Calculate a t-statistic | t |
The original data:
Year | Male | Female | Total |
1971 | 4 | 0 | 4 |
1972 | 4 | 1 | 5 |
1973 | 3 | 0 | 3 |
1974 | 8 | 0 | 8 |
1975 | 15 | 0 | 15 |
1976 | 5 | 0 | 5 |
1977 | 10 | 0 | 10 |
1978 | 6 | 1 | 7 |
1979 | 15 | 2 | 17 |
1980 | 16 | 1 | 17 |
1981 | 13 | 3 | 16 |
1982 | 11 | 1 | 12 |
1983 | 9 | 1 | 10 |