A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 31 tires surveyed, the mean lifespan was 46,300 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim?
A. Give the distribution of X
B. Give the distribution of X̄. Round your standard deviation to 2 decimal places.
C. In words, state what your random variable X represents. Select the letter that best represents your answer.
X represents the average life span, in years, of the tires surveyed.
X represents the number of tires surveyed.
X represents the average life span, in miles, of the tires surveyed.
X represents the life span, in miles, for a tire.
D. What is the test statistic? Round your answer to 2 decimal places. z =
E. What is the p-value? Round your answer to 4 decimal places. p =
F. Answer where question marks are. Based on hypothesis testing and using α = ?, what decision and conclusion can be made:
Given that α ? the null hypothesis as there ? sufficient evidence to conclude that the average life span of the tires is less than 50,000 miles.