Question

A tire company claims that their new tires will have an average life of 139000 miles. A consumer group wishes to test that this claim is not true at the α = 0.05 level of significance. a) Which would be the correct hypotheses for this test? H 0 : μ = 139000 , H A : μ < 139000 H 0 : μ = 139000 , H A : μ ≠ 139000 H 0 : p = 139000 , H A : p ≠ 139000 H 0 : μ = 139000 , H A : μ > 139000 H 0 : p = 139000 , H A : p > 139000 b) A random sample of 58 sets of tires were tested and had an average life of 138900 miles, with a standard deviation of 78.4 miles. Find the test statistic (2 decimal places): c) Give the P-value (4 decimal places, if less than 0.001 answer 0): d) Which is the correct result: Reject the Null Hypothesis Do not Reject the Null Hypothesis e) What is the appropriate conclusion?

Answer 1

a)

H0: = 139000

Ha: 139000

b)

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 138900 - 139000 ) / ( 78.4 / √(58) )
t = -9.71

c)

From T table,

With test statistics of 9.71 and df of 57 ,

p-value = 0

p-value < 0.001

d)

Since p-value < , Reject the null hypothesis.

e)

We conclude that we have sufficient evidence to support the claim that

new tires will have an average life different from 139000 miles.