A two-tailed hypothesis test for H0: μ = 15 at α = .10 is analogous to asking if a 90 percent confidence interval for μ contains 15.

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This is true because a two-tailed hypothesis test with an alpha level of .10 involves splitting the alpha level equally between the two tails of the distribution. This means that there is a 5 percent chance of observing a sample mean that is either smaller or larger than the hypothesized mean of 15, assuming the null hypothesis is true. In other words, a 90 percent confidence interval would contain the hypothesized value if the null hypothesis is not rejected at the .10 level of significance.

A Two-Tailed Hypothesis Test for H0: μ = 15 at α