Question

Researcher investigated whether a new process for producing yarn could reduce the mean amount of volatile organic compounds (VOCs) emitted by carpet. From random samples of carpets, the researchers fund the mean reduction of VOCs emitted by carpets made with yarn produced by the new process compared with that of carpets made with yarn produced by the traditional process was 13 parts per million (ppm). All conditions for inference were met, and the p-value for the appropriate hypothesis test was 0.095. Which of the following statements is the best interpretation of the p-value?
(A) The probability that the null hypothesis is true is 0.095.
(B) The probability that the alternative hypothesis is true is 0.095
(C) The probability of observing a mean reduction of 13 ppm is 0.095.
(D) If the null hypothesis is true, the probability of observing a mean reduction of at least 13 ppm is 0.095
(E) If the null hypothesis is true, the probability of observing a mean reduction of at most 13 ppm is 0.095

Answer 1

Answer:

(D) If the null hypothesis is true, the probability of observing a mean reduction of at least 13 ppm is 0.095

Step-by-step explanation:

The P-value represent the probability of a sample like the one we are testing, given that the null hypothesis is true. In other words, the probablities of getting that sample by pure chance.

That is why if the P-value is smaller than the significance level, it is considered evidence that the null hypothesis is not true.

In this test, the test claim is that new process for producing yarn reduces the mean amount of volatile organic compounds (VOCs) emitted by carpet.

As the reduction is expressed as a positive number, this is an upper-tail test (μ>13 ppm).

Then, the P-value represents then the probability of getting a sample with mean reduction of VOCs of 13 ppm or more, given that the null hypothesis is true.