Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in
x¯¯¯1=290
and
s1=12
, and another random sample of 16 gears from the second supplier results in
x¯¯¯2=321
and
s2=22
. a. Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use α = 0.05, and assume that both populations are normally distributed but the variances are not equal. What is the P-value for this test? b. Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1? Make the same assumptions as in part (a). c. Construct a confidence interval estimate for the difference in mean impact strength, and explain how this interval could be used to answer the question posed regarding supplier-to-supplier differences.