Even though the population standard deviation is unknown, an investigator uses z

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 .05 level of significance. (a) Is the true level of significance larger or smaller than .05? (b) Is the true critical value larger or smaller than that for the critical z ? Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .05 level of significance. (a) Is the true level of significance larger or smaller than .05? (b) Is the true critical value larger or smaller than that for the critical z ? Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .05 level of significance. (a) Is the true level of significance larger or smaller than .05? (b) Is the true critical value larger or smaller than that for the critical z ?

Explanation / Answer

a) the true level of significance larger than .05

b) true critical value is larger than that for the critical z

you can see from table

t* in P(T > t*) = 0.975 is more than z* = 1.96 in P(z> z*) =0.975

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