Question

I have developed a new spray coating that is designed to increase the wear of bicycle tires. To test the new coating, randomly select one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating increases the wear of the bicycle tires. The data is shown below:

Bicycle Coated Tire (C) Non-Coated Tire (N)
1 1.452 0 .785
2 1.634 0.844
: : :
50 1.211 0.954

How should the data be analyzed?
a. Conduct a confidence interval for MUC
b. Conduct an independent samples comparison of MUC-MUN
c. Conduct a test of hypothesis for MUN
d. Conduct a matched pairs comparison of MUC-MUN

Answer 1

To analyze the data, conduct a matched pairs comparison (t-test) of the coated and non-coated bicycle tires to determine if the spray coating significantly affects tire wear.

Step-by-step explanation:

To analyze the data on the new spray coating for bicycle tires, we should consider the design of the experiment, which involves paired differences since each bicycle has one tire with the coating and one without. Hence, the appropriate statistical test is a matched pairs comparison of the mean tread depth left on the coated tire (MUC) and the non-coated tire (MUN). We can calculate the difference in tread depth for each pair of tires and then perform a t-test on these differences to determine if the average difference is significantly different from zero, which would indicate the coating has an effect on tire wear.

Steps for Matched Pairs T-Test

1. Calculate the difference in tread depth for each of the 50 bicycle pairs.
2. Compute the mean and standard deviation of these differences.
3. Formulate the null hypothesis (H0: μD = 0) and the alternative hypothesis (Ha: μD ≠ 0), where μD is the mean of the differences.
4. Use a t-test for the mean of paired differences with α = 0.05.
5. Compare the t-statistic to the critical value from the t-distribution or use the p-value to make a decision.

If the p-value is less than 0.05, or the t-statistic is beyond the critical value, we reject the null hypothesis, indicating that the spray coating has a significant effect on tire wear.