Question: Two samples, each of size n, are taken from a normal distribution with unknown mean and unknown standard deviation . A 90% confidence interval

Two samples, each of size n, are taken from a normal with unknown mean μ and unknown standard deviation σ. A 90% confidence interval for μ is constructed with the first sample, and a 95% confidence interval for μ is constructed with the second. Will the 95% confidence interval necessarily be longer than the 90% confidence interval? Explain.

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