In: Statistics and Probability
a) Identify the claim: state the null and alternative hypotheses. b) Determine the test: left-tailed, right-tailed, or two-tailed. c) Identify the degree of freedom and determine the critical value. d) Graph your bell-shaped curve and label the critical value. e) Find your standardized test statistic ? and label it on your graph. f) Decide whether to reject or fail to reject the null hypothesis. g) Interpret your result.
A trucking firm suspects that the mean life of a certain tire it uses is less than 35,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,350 miles with a standard deviation of 1200 miles. At α = 0.05, test the trucking firm's claim.
a) As we are testing here whether the mean life of a certain tire is less than 35000 miles, therefore the null and the alternative hypothesis here are given as:
b) As we are testing it from the lower side, whether the mean is less than 35000, therefore this is a left-tailed test here.
c) The degrees of freedom here is computed as:
Df = n - 1 = 17
Therefore 17 is the degrees of freedom here.
For 0.05 level of significance, we have from the t distribution
tables here:
P( t17 < -1.740) = 0.05
Therefore -1.740 is the critical value here.
d) The critical value here is shown in the graph as:
e) The t test statistic here is computed as:
This is shown in the graph here as:
f) As the test statistic here lies below the critical value, therefore it lies in the rejection region here and we can reject the null hypothesis here. Therefore Reject H0 is the correct decision here.
g) The interpretation of the result here is that we have sufficient evidence that the mean life of a certain tire it uses is less than 35,000 miles