A psychiatrist is interested in finding a 90% confidence interval for the tics per hour exhibited
by children with Tourette syndrome. The data below show the tics in an observed hour for 13
randomly selected children with Tourette syndrome.
6 10 12 6 0 8 6 8 9 6 9 1 10
Find the 90% confidence interval, the margin of error, and interpret your results.
Standard Deviation, σ: 3.305
Count, N: | 13 |
Sum, Σx: | 91 |
Mean, μ: | 7 |
Calculation
M = 7
Z = 1.64
sM = √(3.32/13) = 0.92
μ = M ± Z(sM)
μ = 7 ± 1.64*0.92
μ = 7 ± 1.51
M = 7, 90%
CI [5.49, 8.51].
The Margin of Error (MOE) is calculated according to the
formula: MOE = z * √p * (1 - p) / √n
Where: z = 1.645 for a confidence level (α) of 90%, p = proportion
(expressed as a decimal), n = sample size.
z = 1.645, p = 0.9, n = 13
MOE = 1.645 * √0.9 * (1 - 0.9) / √13
MOE = 0.494 / 3.606 * 100 = 13.687%
The margin of error is ±13.687%
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