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 8000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the average lifespan was 46,500 miles with a standard deviation of 9800 miles. Do the data support the claim at the 5% level?
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Answer:
No, the data does not support the claim
Step-by-step explanation:
Ho: Mu >/= 50000
Ha: Mu < 50000 (left tailed test)
Since p-value (0.0103) < the alpha value (0.05), the Ho will be rejected
The confidence interval for population mean (Mu) is the
sample mean +/- confidence coefficient*sigma/sqrt n
46700 +/- 1.96 * 8000/sqrt 32
46700 +/- 2772
lower boundary is 46700 - 2772 = 43928
upper boundary is 46700 + 2772 = 49472
The CI is (43928, 49472)
Since the average claimed 50000 is NOT within the boundaries of the CI, it can be inferred that the data does not support the claim of 5% level.
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