Question

An experimental analysis was performed to test the impact of a single factor with four levels (0,1,2,3) on the output. A completely randomized design was employed with ? replications at each level of the input factor. Calculate the value of ? to ensure that the deviation in the estimation of the difference in the mean values of the output at two different levels is within 0.5 units of the mean value using 95% confidence interval. Assume the variance of the output variable (?^2) is equal to 2.

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 0.5, σ = 1.4142

The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.96 * 1.4142/0.5)^2
n = 30.73

Therefore, the sample size needed to satisfy the condition n >= 30.73 and it must be an integer number, we conclude that the minimum required sample size is n = 31
Ans : Sample size, n = 31

r = 31

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