Question

A psychiatrist is interested in finding a 90% confidence interval for the tics per hour exhibited...

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.

Homework Answers

Answer #1

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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