The melting points of two alloys used in formulating solder were investigated by melting 21 samples of

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The melting points of two alloys used in formulating solder were investigated by melting 21 samples of each material. The sample mean and standard deviation for alloy 1 was and , while for alloy 2 they were and .

(a) Do the sample data support the claim that both alloys have the same melting point? Use 0.05 and assume that both populations are normally distributed and have the same standard deviation. Find the P-value for the test.

(b) Suppose that the true mean difference in melting points is 3F. How large a sample would be required to detect this difference using an 0.05 level test with probability at least 0.9? Use 1 2 4 as an initial estimate of the common standard deviation.

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