Question

Assuming that the population is normally distributed, construct a 99% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range. Sample A: 1 3 3 4 5 6 6 8 Sample B: 1 2 3 4 5 6 7 8 Full data set Construct a 99% confidence interval for the population mean for sample A (Type integers or decimals rounded to two decimal places as needed.)

Answer 1

Solution:

Given sample A

1,3,3,4,5,6,6,8

n = Number of Data Values = 8

Sum of Data Values = Σxᵢ = 36

Sample Mean = x̄ = Σxᵢ / n = 36 / 8 = 4.5

s² = Sample Variance = Σ(x_i - x̄)²/(n - 1) = 34/7 = 4.8571

s = Sample Standard Deviation = √ Sample Variance = √4.857 = 2.204

Calculate high end confidence interval total: High End X+ tscorea sAn High End 4.5+ 3.4995 x 2.2048 High End 4.5+3.4995 x 0.77923167286758 High End 45+2.7269212392001 High End 7.23 Calculate low end confidence interval total Low End X- tscore s/n Low End 4.5-3.4995 x 2.204/8 Low End 4.5-3.4995 x 0.77923167286758 Low End 4.5-2.7269212392001 Low End 1.77 Now we have everything display our 99% confidence interval: 1.77 u7.23

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