Question

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 =289.30 and s1=22.5, and another random sample of 16 gears from the second supplier results in =322.10 and s2=21. Use only Table II of Appendix A. (a) Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use the P-value approach, and assume that both populations are normally distributed but the variances are not equal. < 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). < P-value< Is there evidence to support the claim? (c) Construct an appropriate 95% CI on the difference in mean impact strength. Use only Table II of Appendix A. Round your answers to 5 significant digits. CI: ( , ) Does the CI 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? Click if you would like to Show Work for this question: Open Show Work

Answer 1

(a)

From t table the p-value is

0.0005< p-value < 0.0010

Since p-value is less than 0.05 so we reject the null hypothesis.

(b)

From t table the p-value is

p-value < 0.0005

Since p-value is less than 0.05 so we reject the null hypothesis.

(c)

Yes since confidence interval contains -25.