Math Problem Statement
Manufacturers of tires report that tires should be able to last an average of 50,000 miles. A new tire company produces a different type of tread and tests 100 randomly selected tires. This sample of 100 tires lasted an average of 52,000 miles. Assuming the new type of tread does not improve the mileage of the tire, 200 sample means were simulated and displayed on the dotplot.
Using the dotplot and the sample mean mileage, is there convincing evidence that the new type of tread improves the mileage?
Yes, because a mean mileage of 52,000 or more occurred only 7 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
Yes, because a mean mileage of 52,000 or less occurred 193 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 52,000 or less occurred 193 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 52,000 or more occurred 7 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
Solution
The correct answer is:
Yes, because a mean mileage of 52,000 or more occurred only 7 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
Explanation:
In this context, we want to determine if the sample mean of 52,000 miles provides convincing evidence that the new type of tread improves mileage. Since a mean of 52,000 miles or more was observed only 7 times out of 200 simulations, this indicates a low probability (7/200 = 3.5%) of obtaining a mean this high if there were truly no improvement in mileage
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistical Significance
Hypothesis Testing
Sampling Distribution
Formulas
p-value formula for hypothesis testing
Theorems
Central Limit Theorem
Law of Large Numbers
Suitable Grade Level
Grades 10-12