Question 1 - of 1 Step 4 of 6
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An automobile manufacturer has given its jeep a 52.8 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 230 jeeps, they found a mean MPG of 52.7. Assume the population standard deviation is known to be 1.0 . Is there sufficient evidence at the 0.1 level to support the testing firm's claim?

Step 4 of 6: Find the $P$-value of the test statistic. Round your answer to four decimal places.

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Step 1 ：Given values are: sample mean (X) = 52.7, population mean (mu) = 52.8, population standard deviation (sigma) = 1.0, and sample size (n) = 230.

Step 2 ：Calculate the z-score using the formula: \( z = \frac{X - \mu}{\sigma / \sqrt{n}} \).

Step 3 ：Substitute the given values into the formula to get the z-score: \( z = \frac{52.7 - 52.8}{1.0 / \sqrt{230}} \), which gives a z-score of approximately -1.5166.

Step 4 ：Calculate the p-value using the formula: \( p = 2 * \text{sf}(abs(z)) \), where sf is the survival function, which gives the one-sided p-value from the z-score. Since we are doing a two-sided test, we need to multiply the one-sided p-value by 2 to get the two-sided p-value.

Step 5 ：Substitute the calculated z-score into the formula to get the p-value: \( p = 2 * \text{sf}(abs(-1.5166)) \), which gives a p-value of approximately 0.1294.

Step 6 ：Round the p-value to four decimal places to get the final answer: \(\boxed{0.1294}\).