Question

Researchers wish to carry out a test of the null hypothesis that the mean of a certain population is 210 against the alternative hypothesis that it is greater than 210. In their situation, they happen to know the population standard deviation. They feel comfortable assuming normality for this population, and carry out a Z test. They draw a sample of 47 individuals from this population, and find a Z test statistic of 0.77. What is the p-value of the test?

Answer 1

The p-value for a Z test statistic of 0.77 is found by subtracting the cumulative area to the left of the Z score (approximately 0.7794) from 1, which results in a p-value of approximately 0.2206.

Step-by-step explanation:

To calculate the p-value for a Z test, we use the given test statistic and the standard normal distribution. In this scenario, the researchers determined a Z test statistic of 0.77 from a sample of 47 individuals. The p-value is the probability that a Z score is greater than 0.77 when the null hypothesis is true (the population mean is 210).

Using a standard normal distribution table or statistical software, we identify the area to the right of the Z score of 0.77. This area represents the p-value. Since the test is one-sided to the right, we do not need to consider the left tail of the distribution.

The exact p-value can be found by looking up the cumulative area to the left of Z=0.77 and subtracting this value from 1. For a Z score of 0.77, the cumulative area to the left is approximately 0.7794, so the p-value is 1 - 0.7794 = 0.2206.