A gardener is trying to win a competition for the largest pumpkin. Every year, she saves the seeds from the largest pumpkin in her garden. The next year, she plants only those seeds in a large plot. She finds that her pumpkins are becoming larger over the years. Is this an example of natural selection?

No, this is artificial selection. This is because, the selective pressure was not a natural factor, but the farmer who purposefully selected the best seed based on sizes. Therefore, he did not allow the natural phenomenon to it its cause, but rather chose the most fitted / viable/largest seeds to germinate.