Question

The manufacturer of a new racecar engine claims that the proportion of engine failures due to overheating for this new engine, (p1), will be no higher than the proportion of engine failures due to overheating of the old engines, (p2). To test this statement, NASCAR took a random sample of 120 of the new racecar engines and 115 of the old engines. They found that 7 of the new racecar engines and 4 of the old engines failed due to overheating during the test. Does NASCAR have enough evidence to reject the manufacturer's claim about the new racecar engine? Use a significance level of α=0.1 for the test. Step 1 of 6: State the null and alternative hypotheses for the test.

Answer 1

solutions Giren? New engine 7 n = 120 isoo old engine X22 4 h2= 1) = Q=0.10 step! z lorotri nobitro) toe. 10 The null and alternative hypothesis is the Ho Pick Vs Hip > P2 step-2 Test statistics pia 7 120 h) 0.0583 20 Be= X2/n2 = 715 = 0.0348 X + X2 PP (7+4) (120+15) = = 0.0468 nith 25 Z- (p. - 2 ) ✓ TL-P) ( + ni

(0.0583 - 00348) スー 10:0468 (1-0-0468) Protos) 2125 Z- 0.85 10 step-3 miabro 3-4 Critical value! Tool lol to It tult Zx= Zo.lo= 1.2815 - from table rondt co The critical value is 1-2815 151 Step-4 from table p-value = 10.1977 20 The p-value is 10:1937

Steps Decision! and Since. p-value = 0.1977 > R=0:10 20 Zo= 0.85 < Zx-):2815 122 -. Do not reject Ho. - 10 Step 6! Conclusion! 15 Conclude that at the lot level of significance there is insufficient evidence to suggest that the cluim of the proportion of engine failures due to ores eating for engine (p will be no higher than the properties of engine failures due to overheating of the old engines 3). oldit cauf Per pta 20