(i) reject H0 if z -z=-1.645. z =-5.84 < -1.645 then reject H0.
(ii) P-value = P(Z<-5.84)=P(Z>5.84)=0. Since the P-value =0.05, reject H0.
Conclusion: Do not adopt plastic 1.
Example 2 (Exercise 9.2):
Sample sizes are large while population variances are unknown. Notice that this is a two-tailed test.
Test statistics: =4.8462
Decision:
(i) Reject H0 if z -z/2=-1.96 or z z/2 =1.96. z =4.8462 > 1.96 then reject H0.
(ii) P-value = 2P(Z>4.8462)=2(0)=0. Since the P-value =0.05, reject H0.
Conclusion: true average tread lives for two competing brand tires are different.
If you prefer to answer the question computing the confidence interval, 95% confidence interval would become
=(1250.67, 2949.33). You would see that zero does not fall into interval and you would reject H0.
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