A factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. The difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. The p
-value of the test was 0.018.

Which of the following is the correct interpretation of the p-value?

A. If there is a difference of 0.018 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.006.
B. If there is a difference of 0.006 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.018.
C. If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.006 is 0.018.
D. If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at least 0.006 is 0.018.
E. If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at most 0.006 is 0.018.

Hypothesis: The hypothesis must be stated in writing during the proposal state. This will help to keep the research effort focused on the primary objective and create a stronger basis for interpreting the study’s results as compared to a hypothesis that emerges as a result of inspecting the data. the option C is the correct Answer for these Question

The test can be conducted on two basis

Below is the explanation for both of them.

Thus, we conclude that the option C is the correct answer for these question If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.006 is 0.018.

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C) If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.006 is 0.018

Step-by-step explanation:

The given Alternate hypothesis is:

The proportion of defective parts made on the old assembly line is greater than that of the new assembly line.

Therefore, the Null hypothesis would be:

The proportion of defective parts made on the old assembly line is equal to the new assembly line.

The difference between the proportions (old minus new) from the sample data is 0.006 and the p-value is 0.018. We have to choose the correct interpretation of the p-value.

p-value gives the probability of obtaining a result which is as extreme as the one shown by the sample data, assuming the null hypothesis is true.

Since, the Null Hypothesis states that there is no difference in the proportion of defective parts, the correct interpretation of p-value would be:

C) If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.006 is 0.018

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step-by-step explanation: