The number of applications for admission reported by North American Ph

- Number of applications for PhD in art history has declined in last 4 yrs

Conclusion: Interest among recent North American graduates in choosing art history as a career has declined in the last 4 years.

Because PhD applications have declined, we are concluding that interest among recent students to pursue art history as career has declined.

4 options will weaken this while the answer will not.

(A) The number of North American Ph.D. programs in art history that opted to report data about applications for admission has declined in each of the last four years.

This option tells us that fewer programs are reporting data. Hence the data in which our conclusion is based becomes suspect. This weakens our conclusion.

(B) The average age of applicants for admission to North American Ph.D. programs in art history has increased in each of the last four years.

Average age of applicants has increased. First of all, average age of applicants may not say much about more or less interest in art history as a career. Secondly, even if it does say something, it strengthens our conclusion. Conclusion talks about less interest in "recent graduates". So if people applying are older, it means that younger people are LESS interested. This actually supports the conclusion a bit.

(C) The number of errors in data about applications for admission to North American Ph.D. programs in art history has increased substantially during the last four years.

This option tells us that number of errors in data has increased. Hence the data in which our conclusion is based becomes suspect. This weakens our conclusion.

(D) The number of North American employers willing to hire individuals without a Ph.D. for jobs in art history has increased in each of the last four years.

This tells us that in the last 4 years, employers who hire without PhDs has increased. This could be the reason for reduced PhD applicants. Note that it is possible that people's interest has stayed the same or even increased in Art History as a career. Since PhDs are not required nowadays, that could be the reason for fewer PhD applications.
Say, many MBA schools stop requiring GMAT scores for admission. Say, the number of people taking GMAT reduces. Can we say that people's interest in management as career has reduced? No. The need for GMAT has reduced and hence number of people taking it has reduced. It is possible that same or even more number of people have interest in management as a career.
Hence (D) weakens our conclusion that students' interest in art history as a career has reduced.

(E) The percentage of applications for admission received from outside North America by North American Ph.D. programs in art history has declined substantially in the last four years.

This tells us that fewer people from outside NA are applying for PhD programs in art history. That could be the reason for fewer applications to the PhD program. Then it is possible that same or even higher number of NA students are applying for PhD in art history. Hence the interest among NA students for art history as career may be same or may even have increased.
Say 100 students used to apply for PhD 4 yrs ago (50 NA, 50 international). Every year this number has been reducing by 10 so that now only 60 students applied (55NA, 5 international).
Since number of international students has gone down, the total number has gone down but the number of NA students has increased slightly. So can we say that interest among NA graduates has reduced? No. So it does weaken our conclusion.
Hence this weakens our conclusion too.

Answer (B)