Question

Sketch the standard Normal curve for the test statistic and mark off areas under the curve to show why a value of z that is significant at the 1% level in a one-sided test is always significant at the 5% level. If z is significant at the 1% level, what can you say about its significance at the 5% level?

a. A test that is significant at the 1% level is not necessarily significant at the 5% level.
b. A test that is significant at the 5% level coincides with test that is significant at the 1% level.
c. A test that is significant at the 1% level is significant at the 5% level.
d. It is impossible to say anything about it without more information about the data.

Answer 1

A test that is significant at the 1% level is significant at the 5% level.

Step-by-step explanation:

When conducting a hypothesis test using the z-test statistic, the standard Normal curve is often used to determine the significance of the test. The curve is symmetrical and centered at 0, with a standard deviation of 1. To show why a value of z that is significant at the 1% level is always significant at the 5% level, we can mark off areas under the curve. A value of z that is significant at the 1% level means that the observed result is extremely unlikely to occur by chance, with only a 1% chance of it happening. Since the 5% level is less strict than the 1% level, any value of z that is significant at the 1% level will also be significant at the 5% level.

Therefore, the correct answer is option c: A test that is significant at the 1% level is significant at the 5% level.