# MS 150 Statistics Fall 2001 Quiz Nine

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 + 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
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 ³ 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 ³ 30. E =tc*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