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 $H_{0}: p=0.2$ versus $H_{\mathrm{a}}: p

Q: 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 $H_{0}: p=0.2$ versus $H_{\mathrm{a}}: p<0.2$, 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? You may round to three decimal places. P-value $\approx$

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the sample proportion ( $\hat{p}$ ) by dividing the number of parts with errors by the total number of parts sampled. ‖ ‖ step 2 ⋮ $\hat{p} = \frac{70}{400} = 0.175$ ‖ ‖ step 3 ⋮ Identify the z-score from the hypothesis test, which is given as $z = -1.25$. ‖ ‖ step 4 ⋮ Use the standard normal distribution table or a calculator to find the p-value corresponding to the z-score. ‖ ‖ step 5 ⋮ The p-value is the area to the left of $z = -1.25$ in the standard normal distribution. ‖ ‖ step 6 ⋮ Looking up the p-value in the standard normal distribution table or using a calculator, we find that the p-value $\approx 0.1056$. ‖ ‖ step 7 ⋮ Round the p-value to three decimal places as requested. ‖ ‖ step 8 ⋮ P-value $\approx 0.106$. ‖ ∻Answer∻ ⚹ P-value $\approx 0.106$ ⚹ ∻Key Concept∻ ⚹P-value in Hypothesis Testing⚹ ∻Explanation∻ ⚹The p-value represents the probability of obtaining a test statistic as extreme as the one observed, under the assumption that the null hypothesis is true. In this case, it is the probability of observing a z-score of -1.25 or lower if the true proportion of errors is 0.2.⚹◊What is the formula to calculate the p-value for Abdullah's significance test given the test statistic (z⍭ Generate me a similar question◊

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 $H_{0}: p=0.2$ versus $H_{\mathrm{a}}: p<0.2$, 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?
You may round to three decimal places.
P-value $\approx$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the sample proportion ( $\hat{p}$ ) by dividing the number of parts with errors by the total number of parts sampled. ‖ ‖ step 2 ⋮ $\hat{p} = \frac{70}{400} = 0.175$ ‖ ‖ step 3 ⋮ Identify the z-score from the hypothesis test, which is given as $z = -1.25$. ‖ ‖ step 4 ⋮ Use the standard normal distribution table or a calculator to find the p-value corresponding to the z-score. ‖ ‖ step 5 ⋮ The p-value is the area to the left of $z = -1.25$ in the standard normal distribution. ‖ ‖ step 6 ⋮ Looking up the p-value in the standard normal distribution table or using a calculator, we find that the p-value $\approx 0.1056$. ‖ ‖ step 7 ⋮ Round the p-value to three decimal places as requested. ‖ ‖ step 8 ⋮ P-value $\approx 0.106$. ‖ ∻Answer∻ ⚹ P-value $\approx 0.106$ ⚹ ∻Key Concept∻ ⚹P-value in Hypothesis Testing⚹ ∻Explanation∻ ⚹The p-value represents the probability of obtaining a test statistic as extreme as the one observed, under the assumption that the null hypothesis is true. In this case, it is the probability of observing a z-score of -1.25 or lower if the true proportion of errors is 0.2.⚹◊What is the formula to calculate the p-value for Abdullah's significance test given the test statistic (z⍭ Generate me a similar question◊

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