Question

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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 1 = 289.30 and 51 = 22.5, and another random sample of 16 gears from the second supplier results in X2 = 322.60 and $2 = 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 a = 0.05, and assume that both populations are normally distributed but the variances are not equal. Round your answer to 4 decimal places. ka 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. k P-values 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. <M2-Hi < 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? Click if you would like to Show Work for this question: Open Show Work

Answer 1

The test statistic is The p-value is Answer: Given ni = 10 1₂ = 16 x = 289.30, xy = 322.60 S2 = = 21 S, = 22.5, @ The hypothesis test, the supplier a provides with impact strength is higher mean Ho i M₂-M, = 0 Hai Mr-Miso Ja - se t = S2 si + ne 289.30 322.60 (22.5) (21)? + 10 16 33.3 8. 8424 Z = 3. 7659 are degrees of freedom 2 ( + sal n2 df ni (si n2 + n2-1 ((22.53€ (212 (937) (9215) |(21)? 10 16 16-1 10-1

6113. 2852 df - 335. 4117 - 18.2262 ~19 0.05 df =19 t = 3.7659, az P-value = 0.0007 (from t-table) The po value (0.0007) < x 10,05) thuy, the null hypothesis is rejected at 5% level of significance. → Thus, there ir significant supplies e provides gears with highes mean 0 evidence to support the claim that the imtact strength. o Ho i M₂-M, 225 Hai Mz-M, z 25 Test statistic is (2-)-(M2-40) t 5,2 + ni n2 - (322.60-289-30) - 25 (22.5)2 (21)² t 16 10 8.3 8.8424 1 0.9387 t = 0.9387

The Р value is df = 19, d;0.05, t> 0.9387 the P-value = 0.1798 (from t- table the p-value (0.1798) < 2 (0.05) thus, the null hypothesis ů not rejected at 5% level of significance. → thus, there is not significant evidence to support claim that the supplies a provides gears with mean impact strength at least as foot-pounds higher than supplies (7 to critical value is tas idf te= toios 19 21 > to.025, 19 tes 2.093 t-table) (from t 959. confidence interval is = R₂-2, I te 5,2 saž + ne nu ci I (22.5)2 (20) I 2.093 + 2132 322.60-289-30) I lo 16 Co I > 33.3 I 2.093 * 8.8424 2 33. 3 7 18. 5071 = 14.7929, 51.807) = 14.793, 51.807. " The 95%. c.I for the difference between the mean impact strength for supplier I and 2 å 14.793 5M 51.807. Thus supporting the claim that the supplies 2 provides gears with mean impact strength at least as foot-pounds higher than supplier , 25 is contained in the confidence interval. SO