Question

One of the many concerns of college students today is the time required for them to graduate with a baccalaureate degree (BA or BS). Current estimates in the California public university system is that takes an average of slightly over 5 years for a student to complete a baccalaureate degree. One researcher suggests that males take a significantly longer average time than females to complete a baccalaureate degree. What is the correct hypotheses to test in an attempt to support the claim of this researcher? Let μ1 represent the average time it takes females to complete a baccalaureate degree in the California public university system, and let μ2 represent the average time it takes males to complete a baccalaureate degree in the California public university system.

Select one:

A. H0:μ1−μ2=0

Ha:μ1−μ2>0

B. H0:μ1−μ2=0

Ha:μ1−μ2<0

C. H0:μ1−μ2=0

Ha:μ1−μ2≠0

D. H0:μ1−μ2>0

Ha:μ1−μ2≠0

E. None of the above

Answer 1

Solution:

Given:

μ1: the average time it takes FEMALES to complete a baccalaureate degree in the California public university system, and

μ2: the average time it takes MALES to complete a baccalaureate degree in the California public university system.

We have to test if " MALES take a significantly longer average time than FEMALES to complete a baccalaureate degree".

That is: "FEMALES take a significantly shorter average time than MALES to complete a baccalaureate degree".

That is: Mean of FEMALES < Mean of EMALES

That is we have to test: μ1 <  μ2.

That is we have to test: μ1 -  μ2 < 0.

Thus correct answer is:

B.

H₀ : μ₁−μ₂ = 0

H_a : μ₁−μ₂ < 0

Note: Under null hypothesis H0, we always state difference is equal to null or 0.

Alternative hypothesis Ha is either < or > or ≠ depending on claim stated.