8.7 Let denote the true average tread life of a certain type of tire. Consider t

Question

8.7 Let denote the true average tread life of a certain type of tire. Consider testing Ho: = 30,000 versus Ha: > 30,000 based on a sample of size n = 16 from a normal population distribution with = 1500. A test with =.01 requires z.01 = 2.33. The probability of making a type II error when = 31,000 is 30,000 31,000 1500/V16 Since zi = 1.28, the requirement that the level .01 test also have (31,000,-.1 (31.000)= (2.33 + 30,1 0)-w-34)- 3609 (31,000) = 412.33 + = (.34) = .3669 necessitates 1500(2.33 + 1.28)] 30,000 31,000 The sample size must be an integer, so n = 30 tires should be used. = (-5.42) 29.32

Explanation / Answer

17.a

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   30000  
Ha:    u   >   30000  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    +   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    30960          
uo = hypothesized mean =    30000          
n = sample size =    16          
s = standard deviation =    1500          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.56          
              
Also, the p value is              
              
p =    0.005233608          
              
As z > 2.326, and P < 0.01, we   REJECT THE NULL HYPOTHESIS.   [DECISION]      

Related Questions

Navigate

• Browse (All)
• Browse 8
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.