Suppose that a random sample consisting of 16 observations is available from the normal distribution for which both the mean μ1 and the variance σ21 are unknown, and an independent random sample consisting of 10 observations is available from the normal distribution for which both the mean μ2 and the variance σ22 are also unknown. For each constant r > 0, construct a test of the following hypotheses at the level of significance 0.05:

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