Question

In: Statistics and Probability

A tow truck company suspects that the lifespan of certain tires is less than the 28,000 miles they were offered.

 

A tow truck company suspects that the lifespan of certain tires is less than the 28,000 miles they were offered. To verify if its suspicion is true, the company purchases 40 tires, places them in its trucks and measures the life of each one. The results are presented in the rate below. Presumed known standard deviation = 1300 miles

26579 27965 26868 25070 26488
25834 27355 28039 32237 25523
28331 29103 24439 32850 28942
27474 27618 25645 27497 28183
27475 27697 28524 27704 26873
27232 31633 29363 26857 28017
27396 26982 28007 26293 25828
28256 25679 22594 31000 24208

If we perform a hypothesis test with α = 0.1,

to. What can we conclude? Is the company correct in its suspicions? Respond based on evidence - Clearly define hypotheses, areas of acceptance and rejection, test statistic and CONCLUDE in complete sentence

b. If we wanted to construct a confidence interval for µ with an error of not more than 25 miles, what sample size should we use?

c. If the actual average is 27,800 miles, what would be the probability of making a type II error? What would it mean in this case to make a type II error?

Solutions

Expert Solution

26579
25834
28331
27474
27475
27232
27396
28256
27965
27355
29103
27618
27697
31633
26982
25679
26868
28039
24439
25645
28524
29363
28007
22594
25070
32237
32850
27497
27704
26857
26293
31000
26488
25523
28942
28183
26873
28017
25828
24208

a.

Mean = 27491.45 miles, standard deviation = 1300 miles

Ho: The lifespan of certain tires is equal to the 28,000 miles

H1: The lifespan of certain tires is less than the 28,000 miles

Then, = = -2.474

Then, t(39,0.1) = -1.304 (one-tailed)

Here, -2.474 < -1.304

So, we reject Ho or can say that the lifespan of certain tires is less than the 28,000 miles.

b. Now, error = 25 miles = t*s/sqrt(n) ; sqrt(n) = 1.304 * 1300 / 25 ; n= 4597.92 or 4598 trucks will be inspected

c. At apha = 0.1, and actual mean 27800, cohen's d = 0.24

then, beta = 1 - 0.82 = 0.18 (i am not sure for this one, do let me know)

 

orchestra answered 1 year ago
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