Question

A sample of 10 was taken from an in-control. A variance of 4.2 and a mean 23.2 were calculated. Determine the 95% confidence interval on the mean and standard deviation.

Answer is CI=(21.734, 24.666)

Explain any potential problems with this analysis. I only need the explanation of potential problems! No need to do the calculations. I already have the calculation.

ONLY EXPLAIN POTENTIAL PROBLEMS WITH THIS ANALYSIS.

Answer 1

The potential problems with given analysis are described as below:

1) The sample size for the analysis is given as 10. This sample size is comparatively very small. For the large sample sizes, we get the more reliable estimates or results for the confidence intervals for the mean and standard deviation. The sampling error should be minimized for getting better results.

2) If the sample data consist of an outlier, then there would be potential problem in the analysis; because we would not get unbiased estimates for the population due to outliers in the sample.

3) If the sample is not taken from the normally distributed population, then there would be potential problem in the given analysis for the confidence intervals for the population mean and population standard deviation. The given confidence intervals are constructed on the assumption of normal populations.

4) If the sample data is skewed in nature, then there would be potential problem in the calculation of confidence intervals and it will provide biased estimates for the confidence intervals.

5) If the sample data is not selected by using proper random sampling method, then estimates for the confidence intervals would not be unbiased for lower and upper limits.