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1. The question asks us to identify the assumption for the conclusion and a statement that weakens the conclusion.

2. First, let's identify the conclusion: instituting yoga classes and self-help seminars at both libraries most likely resulted in a 5% higher patronage (in a year).

3. Now, we can go through each of the following statements and see if they work:

- This past year, both libraries have instituted a very popular "story hour" program during which librarians read to children and encourage them to read more books at home. In other words, there is another factor that has directly resulted in a higher patronage, which means that the yoga classes and self-help seminars may have no influence. So, this statement weakens the conclusion.

- Patronage at Library A has traditionally been higher than at Library B. Our conclusion is not interested in any data comparing the two libraries. So, this statement is neither.

- Attendees of the yoga classes and self-help seminars check out books that they would not have checked out had they not attended the classes and seminars. This would show that instituting them does directly increase patronage, which is needed for the conclusion. So, this statement is the assumption needed.

- The yoga classes have been better attended than the self-help seminars. Once again, the conclusion is not interested in any comparisons between what was instituted. So, this statement is neither.

- If patronage were measured by the number of DVDs checked out, rather than by the number of books checked out, both libraries would show increasing patronage numbers over the past five years. The conclusion is based on the current definition of patronage, which is on the number of books. So, this statement is neither.

- An increase in patronage means that the libraries will not lose the funding, vital to their operating budget, that they currently receive from a private foundation. Although funding might help explain the changes in patronage and vice versa, there is no other data we can use. So, this statement is neither.
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Response:

"there is an improvement in patronage owing to instituting yoga classes and self-help seminars at both libraries".

This past year, both libraries have instituted a very popular "story hour" program during which librarians read to children and encourage them to read more books at home. Directly weakens the statement as it brings out another parameter linked to the increase in patronage, not being yoga classes and self-help seminars. Therefore, this statement weakens the conclusion.

Patronage at Library A has traditionally been higher than at Library B. Irrelevant, does not weaken or strengthen.

Attendees of the yoga classes and self-help seminars check out books that they would not have checked out had they not attended the classes and seminars. Supports the conclusion, as this is the underlying assumption.

The yoga classes have been better attended than the self-help seminars. Irrelevant, does not weaken or strengthen.
If patronage were measured by the number of DVDs checked out, rather than by the number of books checked out, both libraries would show increasing patronage numbers over the past five years.

An increase in patronage means that the libraries will not lose the funding, vital to their operating budget, that they currently receive from a private foundation. [color=#e82a1f]Irrelevant, does not weaken or strengthen.
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