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Suppose you conduct a lower-tail z-test on the mean of normal population and get a test statistic of 0.09. The P-value for this z-test is _________ using the z-table provided in this course.

Question

Suppose you conduct a lower-tail z-test on the mean of normal population and get a test statistic of 0.09. The P-value for this z-test is _________ using the z-table provided in this course.

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Solution

To find the P-value for a lower-tail z-test, we need to look up the z-score in the standard normal distribution table (z-table).

Step 1: Look up the z-score in the z-table. The z-table gives us the probability that a standard normal random variable is less than or equal to a given value. In this case, our z-score is 0.09.

Step 2: Find the corresponding probability in the z-table. Looking up 0.09 in the z-table, we find a probability of 0.5359. This means that approximately 53.59% of the data falls below a z-score of 0.09.

Step 3: Calculate the P-value. Since this is a lower-tail test, the P-value is the probability that we found in the z-table. Therefore, the P-value for this z-test is 0.5359.

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