An important situation is when \u03b4 0 whether the two means are equal Example 77

An important situation is when δ 0 whether the two

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An important situation is when δ= 0: whether the two means are equal. Example 7.7.To compare the mean calcium concentrations at two stations (downstream and upstream), random samples of 20 and 15 measurements are taken respectively at the downstream station and the upstream station. The resulted means are 21.3 and 14.2 milligrams per cubic decameter. It is known that the two populations are normal with st dev’s 1.8 and 2.4 respectively, and the two samples are independent. (a) Do the data provide sufficient evidence at 1% level that the mean calcium concentration is higher at the downstream station than at the upstream station? (b) If the evidence in (a) is sufficient, do the data also suggest at 1% level of significance that the mean calcium concentration at downstream station exceeds that of the upstream station by more than 5 milligrams? (c) Find a 98% C.I. for μ1 μ2. Discuss the connections between the results in (b) and (c). 23
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Solution: = 2.326 2 > 5 24
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2 2 2 1 2 25
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Example 7.8.Reconsider Example 6.16. Perform a test of the hypothesis that the average starting salaries offered to new B.A. recipients at two universities are same against the alternative hypothesis that they are different. Use α= 0.05. Is the conclusion consistent with that of Example 6.16? μ 2
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= π ) . α 2 Z α Z α
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