Find the necessary confidence interval for a population mean 𝜇 for the following values. (Round your answers to two decimal places.) 𝛼 = 0.01, n = 32, x = 31, s2 = 16

Answer 1

As the significance level is α=0.01, this corresponds to a 99% confidence level. With a sample size of n=32 being greater than 30, it's best to determine the z-statistic (assuming conditions are all met). The standard deviation would be s=4 because the variance is given as s²=16 and z=2.807 because of the 99% confidence level:

CI = x̄ ± z(s/√n)

CI = 31 ± 2.807(4/√32)

CI = {29.02, 32.98}

Therefore, the necessary confidence interval for the population mean μ is {29.02, 32.98}.

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