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 xbar.gif (842 bytes) = 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 xbar.gif (842 bytes) Sx/n =AVERAGE(data)
Sample standard deviation sx sampstdev.gif (1072 bytes) =STDEV(data)
Normal Statistics
Calculate a z value from an x z = standardize.gif (905 bytes) =STANDARDIZE(x, m, s)
Calculate an x value from a z x = s z + m = s*z+m
Calculate a z value from an xbar.gif (842 bytes) z xbartoz.gif (1022 bytes)
Calculate an xbar.gif (842 bytes) from a z xbarfromz.gif (1060 bytes) =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 error_tolerance_zc.gif (989 bytes) =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 error_tolerance_tc.gif (989 bytes) =tc*sx/SQRT(n)
Calculate a confidence interval for a population mean m from a sample mean xbar.gif (842 bytes) and an error tolerance E xbar.gif (842 bytes)-E< m <xbar.gif (842 bytes)+E
Hypothesis Testing
Calculate a t-statistic t xbartot.gif (1028 bytes)

left_to_z_small.gif (2653 bytes)

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

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