Final answer:
Option a) -1.64 and 1.97 is correct. The 95% matched paired t-interval indicates that Brand A shoes last between -1.64 and 1.97 weeks longer than Brand B shoes, allowing both shorter and longer durations for Brand A.
Step-by-step explanation:
The question is asking for the range of weeks that Brand A shoes are expected to last longer than Brand B shoes based on a 95% matched paired t-interval. The interval calculated was (-1.64, 1.97). The negative value in the interval implies that Brand A shoes can last shorter than Brand B shoes, meaning this interval includes negative, zero, and positive differences in the mean lifespan. However, a positive value means Brand A shoes last longer. Therefore, the sample of Brand A shoes was found to last between -1.64 weeks and 1.97 weeks longer than Brand B, suggesting that sometimes they can last slightly less time (up to 1.64 weeks) and other times more (up to 1.97 weeks). The correct option is therefore a) -1.64 and 1.97.