Assuming that the population is normally distributed, construct 95% co | Basic Statistics 0

Basic Statistics05 marksNumerical: confidence interval meanConfidence interval for population mean

Assuming that the population is normally distributed, construct 95% confidence interval for the population mean using the following sample data. 1, 2, 3, 4, 5, 20. Again in the same data set, replace the value of 20 by 6, then compute the confidence interval for the mean. Explain why there is considerable difference in the confidence interval? [5]

Dataset A: $1, 2, 3, 4, 5, 20$ with $n = 6$ - Dataset B (20 replaced by 6): $1, 2, 3, 4, 5, 6$ with $n = 6$ - Confidence level: 95%, so $\alpha = 0.05$ - Population assumed normal, $\sigma$ unknown, small sample $\Rightarrow$ use $t$ -distribution with $df = n - 1 = 5$ - $t{0.025, 5} = 2.571$ --...

Dataset A: $1, 2, 3, 4, 5, 20$ with $n = 6$ - Dataset B (20 replaced by 6): $1, 2, 3, 4, 5, 6$ with $n = 6$ - Confidence level: 95%, so $\alpha = 0.05$ - Population assumed normal, $\sigma$ unknown, small sample $\Rightarrow$ use $t$-distribution with $df = n - 1 = 5$ - $t{0.025, 5} = 2.571$ --...

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