A shoe manufacturer wants potential customers to compare two types of shoes, one made of the current PVC material \(X\) and one made of a new PVC material \(Y\). Shoes made of both are available. Each person, in a sample of 52, is asked to wear one pair of each type for a whole day. After a walk of \(2 \mathrm{~km}\), they are asked to score that day's pair on a scale of 1 to 10 , with higher scores being better. The differences in scores

\[(\text { New PVC } Y)-(\text { Current PVC } X)\]

have mean 2.6 and variance 3.9. Construct a \(90 \%\) confidence interval for the mean difference.