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Chapter 9: Q.74 (page 543)

A particular brand of tires claims that its deluxe tire averages at least 50,000miles 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. From the 28tires surveyed, the mean lifespan was 46,500miles with a standard deviation of 9,800miles. Using alpha =0.05, is the data highly inconsistent with the claim?

Short Answer

Expert verified

No, the data is not highly inconsistent with the claim.

Step by step solution

01

Given Information

Null hypothesis H0: μ≥50000

Alternate Hypothesis (Hα):μ<50000,it is left-tailed test

02

Explanation

Since the p-value (0.0130)<the alpha value(0.05), the H0 value is rejected.

The Confidence Interval (CI) for population mean (μ)is:

sample mean

=46700±1.96×80032

=46700±2772

03

Conclusion

Lower boundary is 46700-2772=43928

Upper boundary is 46700+2772=49472

The CI is (43928,49472)

Since the claimed average of 50000does not fall within boundaries of the confidence interval , the inference that the data does not support the claim of 5%level could be drawn.

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Most popular questions from this chapter

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening

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