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# How do I find the P-value?

The manufacturer of a particular brand of tires claims they average 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the tire's lifespan has a Normal distribution with population standard deviation of 8,000 miles.

You believe that the manufacturer is lying, and the lifespan of the tires is less than 50,000 miles. You conduct a survey of 26 tire owners. In your survey data, the mean lifespan was 48500 miles. Using alpha = 0.05, can you prove that the data are inconsistent with the manufacturer's claim?

μ=50000

μ<50000

H0: μ=50000

Ha: μ<50000

Test stastistic= -.9561

How do I find the P-value?

### 1 Answer

- az_lenderLv 72 months ago
Standard error of the sample mean = (8000 mi)/sqrt(26) = 1568.93.

Z = (48500 - 50000)/1568.93 = -0.95607, I agree with you.

For a one-tailed test at alpha = 0.05, the absolute value of the z-score of the result must exceed 1.645. In your problem, |z| < 1.0, so you FAIL to reject the null hypothesis.

In other words, the data are reasonably consistent with the manufacturer's claim.