Answer Happy

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 xˉ1​=289.30 and s1​=22.5, and another random sample of 16 gears from the second supplier results in xˉ2​=321.50 and s2​=21. Use only Table V of Appendix A. (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. Round your answer to 4 decimal places. <P-value < Is there evidence to support the claim?
(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 ? Find bounds on the P-value making the same assumptions as in part (a). Round your answer to 2 decimal places. <P-value < Is there evidence to support the claim? (c) Construct an appropriate 95% confidence interval on the difference in mean impact strength. Use only Table V of Appendix A. Round your answers to 3 decimal places. Does the confidence interval 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 ?