The p-value for a simple random sample of 100 with a hypothesis of 9, a sample average of 8.3, and a standard deviation of 4.3 can be found by calculating the z-score and using a standard normal distribution table or a calculator.
In this case, the z-score is calculated as:z = (8.3 - 9) / (4.3 / √100)z = -0.7 / 0.43z = -1.627This z-score corresponds to an area of 0.0516 under the standard normal distribution curve. This means that the probability of obtaining a sample mean of 8.3 or less, assuming the true population mean is 9, is 0.0516 or 5.16%.
Since this is a two-tailed test (we are interested in the probability of getting a sample mean as extreme as 8.3 or less or as extreme as 9.7 or more), we need to double the probability to get the p-value:p-value = 2 * 0.0516p-value = 0.1032Therefore, the p-value for this hypothesis test is 0.1032.
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