How large a sample is required if we want to have 95% confidence that the averag

Question

How large a sample is required if we want to have 95% confidence that the average hardness of a sample of shafts is within 0.3 (margin of error) of the expected value if the variance is known to be 1.0, 2.0, 3.0, 4.0, 5.0, 6.0? Using the Excel spreadsheet to plot the relationship between the sample size (Y-axis) vs. standard deviation (sigma). If the observed concentration readings are 1.27, 1.33, 1.19, and 1.24, determine 95% confidence interval for the mean concentration assuming variance = 0.003. Prove: E(S^2) = sigma^2, please show each step to demonstrate how you prove it.

Explanation / Answer

1. Here it is given that we need to find sample size for 95% CI, so z =1.96 where E=0.3

Formula for sample size is n=(z*sd/E)^2

For difference value of sd we will find n as below

sd n

1 42.68=43

1.41 84.86=85

1.73 127.75=128

2 170.73=171

2.24 214

2.45 256

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