The following table summarizes data for Sales per Week for random samples of supermarkets, in $100,000s. The weeks correspond to weeks of an advertising campaign. In advance, it was decided that the only hypothesis to be tested is that there is a linear trend in the data. Test the null hypothesis of no linear trend at the 0.05 significance level.

Note that using table A.6, we find that the coefficients of contrast for linear trend are 2, 1, 0, 1, 2. Let _i denote the mean sales per week when the advertising campaign holds for i weeks. Then the linear contrast is L = 2_{1 2} + ₄ + 2₅.

week	n	mean sales	standard deviation
1	10	18.6	5.9
2	10	23.4	6.2
3	10	21.8	6.0
4	10	22.6	5.8
5	10	26.2	6.1