Question

In the statement z = 3.14, p < 0.05, which of the following interpretations is TRUE? a. There is a marginally significant difference between the sample value and the population. b. There is a significant difference between the sample value and the population. c. There is not a significant difference between the sample value and the population. d. The answer cannot be determined from the information given.

Answer 1

Explanation:

The statement "z = 3.14, p < 0.05" suggests that a z-test was performed and the resulting z-value is 3.14, with a corresponding p-value less than 0.05.

Based on this information, the interpretation that is TRUE is:

b. There is a significant difference between the sample value and the population.

A p-value less than 0.05 indicates that the probability of obtaining a z-value as extreme or more extreme than 3.14 under the null hypothesis is less than 5%. This suggests strong evidence against the null hypothesis, which typically assumes no difference between the sample value and the population. Therefore, we can conclude that there is a significant difference between the sample value and the population.