Question

Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .01 level of significance. In this situation the true level of significance of this test is:

smaller than .01

unknown

larger than .01

equal to .01

Answer 1

Even when the population standard deviation is unknown, we are using here Z test instead of t test, this means that we are using lower value of the p-value here instead of the real value. This is because for the same test statistic value, we get a higher p-value for t test than in case of Z test. Therefore we would be actually rejecting the null hypothesis at a higher level of significance than the given value of 0.01. Therefore larger than 0.01 is the correct answer here