Refer to the JOM (Jan. 2003) comparison of a new high-strength RAA aluminum alloy to the current strongest aluminum alloy, Exercise 7.43. Suppose the researchers want to estimate the difference between the mean yield strengths of the two alloys to within 15 MPa using a 95% confidence interval. How many alloy specimens of each type must be tested in order to obtain the desired estimate?

Data from Exercise 7.43

Mechanical engineers have developed a new high-strength aluminum alloy for use in antisubmarine aircraft, tankers, and long-range bombers. (JOM, Jan. 2003.) The new alloy is obtained by applying a retrogression and reaging (RAA) heat treatment to the current strongest aluminum alloy. A series of strength tests were conducted to compare the new RAA alloy to the current strongest alloy. Three specimens of each type of aluminum alloy were produced and the yield strength (measured in mega-pascals, MPa) of each specimen determined. The results are summarized in the table.

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Alloy Type RAA Current Number of specimens 3 3 Mean yield strength (MPa) 641.0 592.7 Standard deviation 19.3 12.4