Question

a tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. now the company is advertising that their new tires' life expectancy has increased. in order to test the legitimacy of their advertising campaign, an independent testing agency tested a sample of 90 of their tires. the agency found the mean of the 90 tires to be 27,000 miles and the standard deviation to be 3,990 miles. use a 0.01 level of significance and test to determine whether the company is using legitimate advertising. show all seven steps

Answer 1

a)

H0: = 26000

Ha: > 26000

b)

Type of test - This is right tailed test.

c)

df = n -1 = 90 - 1 = 89

t critical value at 0.01 level with 89 df = 2.369

Decision rule = Reject H0 if t > 2.369

d)

Test statistics

t = ( - ) / (S / sqrt(n) )

= (27000 - 26000) / (3990 / sqrt(90) )  

= 2.38

e)

decision - Since test statistics falls in rejection region, Reject H0.

f)

p-value = ?

From T table,

With test statistics of 2.38 and df of 89,

p-value = 0.0097

g)

Conclusion - We have sufficient evidence to support the claim that their new tires' life expectancy has increased.