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[Solution Library] A sample of size 100 has a sample mean of X̄ and sample standard deviation of 0.2. In terms of X̄, find the 95 \% confidence interval for the

Question: A sample of size 100 has a sample mean of \(\bar{X}\) and sample standard deviation of 0.2.

  1. In terms of \(\bar{X}\), find the \(95 \%\) confidence interval for the population mean.

What condition must \(\bar{X}\) satisfy for you to reject the null hypothesis in favor of the alternative hypothesis in the following two cases?

  1. \(\begin{aligned} & {{H}_{0}}:\mu =20 \\ & {{H}_{A}}:\mu \ne 20 \\ \end{aligned}\)
\(\begin{aligned} & {{H}_{0}}:\mu =20 \\ & {{H}_{A}}:\mu >20 \\ \end{aligned}\)

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