Question

Abdullah is a quality control expert at a factory that paints car parts. He knew that the factory was painting 20% of the parts with an error, so he made a change in the painting process. After the change, he wanted to test H₀ : p = 0.2 versus Hₐ : p<0.2, where p is the proportion of parts that the factory was painting with an error. Abdullah took a sample of 400 parts and found that 70 had an error, and the corresponding test statistic was z = -1.25.

Assuming that the necessary conditions are met, what is the approximate P-value for Abdullah's significance test?

Answer 1

Abdullah's test statistic of z = -1.25 is used to find the P-value in the standard normal distribution table, and if this P-value is less than the chosen significance level (often 0.05), it would suggest the error rate in painting parts has decreased.

Step-by-step explanation:

Abdullah is a quality control expert at a factory that paints car parts. He observed that previously, 20% of the parts were painted with an error. After implementing a change, he conducted a hypothesis test to see if the error rate had decreased, testing H₀ : p = 0.2 against H₁ : p<0.2.

With a sample of 400 parts, 70 were found to have errors, resulting in a test statistic of z = -1.25. To find the approximate P-value for Abdullah's significance test, one would look up the z-score in the standard normal distribution table. This value gives the probability of observing a z-score of -1.25 or less assuming the null hypothesis is true.

While the exact P-value isn't provided here, assuming the necessary conditions are met, this P-value would be compared against a significance level, often α = 0.05, to decide whether to reject the null hypothesis. If the P-value is less than α, the null hypothesis would be rejected, indicating that the error rate has decreased.