Final answer:
To calculate the p-value, we use the test statistic (z-statistic) of 2.18 and reference the Standard Normal Table to find the cumulative area to the left, which is 0.9852. Subtracting this from 1, we get a p-value of 0.0148, representing the probability of observing a statistic as extreme as ours under the null hypothesis.
Step-by-step explanation:
Calculating P-value Using a Z-Statistic
To calculate the p-value of our z-statistic using the Standard Normal Table, we need to first establish the z-statistic from the given data. According to the information provided, our test statistic rounded to two decimal places is 2.18. Now, to find the p-value corresponding to this z-statistic, we look up the z-score in the Standard Normal Table, which shows the area under the normal curve to the left of our z-score. As most z-tables provide the cumulative area to the left, we need to subtract this value from 1 to find the right-tail area which is our p-value.
Considering the given z-statistic of 2.18, the Standard Normal Table provides us with an area to the left of 0.9852. Therefore, the p-value can be calculated by subtracting this from 1, which results in 0.0148. This is the area in the right tail, representing the p-value for our one-sided hypothesis test.
In summary, the p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one observed, given that the null hypothesis is true. The smaller the p-value, the stronger the evidence against the null hypothesis.