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Please help me interpret the p-value!

When Carter bought his new laptop computer, the sales person told him that the average battery life was 5 hours and that the number of hours of battery life is approximately normally distributed. After using the computer for a few days, Carter began to have his doubts. The next 10 times that Carter used his computer, he kept track of how long it took for the battery to drain. The sample average was 4.25.

Conducting a one-sided significance test, he found the p-value to be 0.038.

What is the best way to interpret this p-value in the context of this situation?

Select one answer

A A p-value as small as 0.038 gives Carter good reason to doubt that the average battery life of his. laptop really is 5 hours.

B If the average battery life really is 5 hours, then a sample of 10 observations having a sample mean of 4.25 hours or lower would only occur about 3.8% of the line.

C When 10 observations are made, the battery life will be as low as 4.25 hours in 3.8% of the observations.

D There is a 3.8% chance that Carter's laptop computer battery will last for 4.25 hours anytime he uses it.

E Only 3.8% of all alptip batteries will last as long as 5 hours.​

Sagot :

The correct interpretation of the p-value is given by:

B If the average battery life really is 5 hours, then a sample of 10 observations having a sample mean of 4.25 hours or lower would only occur about 3.8% of the line.

How to find the p-value of a test?

It depends on the test statistic z, as follows:

  • For a left-tailed test, it is the area under the normal curve to the left of z, which is the p-value of z.
  • For a right-tailed test, it is the area under the normal curve to the right of z, which is 1 subtracted by the p-value of z.
  • For a two-tailed test, it is the area under the normal curve to the left of -z combined with the area to the right of z, hence it is 2 multiplied by 1 subtracted by the p-value of z, which means that the p-value for a two-tailed test is twice the p-value of a one-tailed test.

In this problem, a left-tailed test is used, as we are testing if the mean is less than 5 hours.

The sample mean from the 10 times was of 4.25, and the p-value is of 0.038, which means that the area to the left of Z under the normal curve is of 0.038, that is, a sample mean of 4.25 hours or lower would only occur about 3.8% of the line, hence option B is correct.

You can learn more about p-values at brainly.com/question/13873630

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