Question

A university wants to estimate the mean GPA for first-year graduate students. If the mean population standard deviation is 1.1, how large must a sample be to estimate the mean GPA to within 0.15 with 98% confidence?

Answer 1

The following information is provided,
Significance Level, α = 0.02, Margin or Error, E = 0.15, σ = 1.1

The critical value for significance level, α = 0.02 is 2.33.

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 = (2.33 * 1.1/0.15)^2
n = 291.95

Therefore, the sample size needed to satisfy the condition n >= 291.95 and it must be an integer number, we conclude that the minimum required sample size is n = 292
Ans : Sample size, n = 292

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