. A test is conducted to compare the tread wear of certain type of tires on highways paved with asphalt and highways paved with concrete. Road tests were conducted with the same type of tires on two types of highways. Summary data on the mileage of the tires up to a certain level of wear are given below. Sample Size Sample Mean Sample Standard Dev. Asphalt 35 29,700 9,700 Concrete 35 25,500 7,800 Does this information suggest that tires wear faster on concrete-paved highways than asphalt paved highways? Test using = 0.01. Use the 5 step method.
Question
. A test is conducted to compare the tread wear of certain type of tires on highways paved with asphalt and highways paved with concrete. Road tests were conducted with the same type of tires on two types of highways. Summary data on the mileage of the tires up to a certain level of wear are given below. Sample Size Sample Mean Sample Standard Dev. Asphalt 35 29,700 9,700 Concrete 35 25,500 7,800 Does this information suggest that tires wear faster on concrete-paved highways than asphalt paved highways? Test using = 0.01. Use the 5 step method.
Solution
Sure, let's use the 5 step hypothesis testing method to answer this question.
Step 1: State the null hypothesis (H0) and the alternative hypothesis (H1). H0: μ1 - μ2 ≤ 0 (The mean tire wear on asphalt-paved highways is equal to or greater than on concrete-paved highways) H1: μ1 - μ2 > 0 (The mean tire wear on asphalt-paved highways is less than on concrete-paved highways)
Step 2: Choose the significance level, α. α = 0.01
Step 3: Identify the test statistic. Since we have two independent samples and we know their standard deviations, we can use the two-sample z-test.
Step 4: Formulate the decision rule. If the z score calculated from the test statistic is greater than the critical z value from the z table (which corresponds to the significance level of 0.01), we reject the null hypothesis.
Step 5: Take a sample and arrive at a decision. First, calculate the pooled standard deviation: sp = sqrt[((n1-1)*s1^2 + (n2-1)*s2^2] / (n1+n2-2)] = sqrt[((35-1)*9700^2 + (35-1)*7800^2] / (35+35-2)] = 8,747.5
Then, calculate the z score: z = (x1 - x2) / (sp * sqrt(1/n1 + 1/n2)) = (29700 - 25500) / (8747.5 * sqrt(1/35 + 1/35)) = 2.02
The critical z value for a one-tailed test at the 0.01 significance level is 2.33. Since our calculated z score (2.02) is less than the critical z value (2.33), we fail to reject the null hypothesis.
Conclusion: The data does not provide enough evidence to suggest that tires wear faster on concrete-paved highways than on asphalt-paved highways at the 0.01 significance level.
Similar Questions
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