With reference to Example 5, test the null hypothesis σ₁ - σ₂ = 0 against the alternative hypothesis σ₁ - σ₂ > 0 at the 0.05 level of significance.

Example

In the comparison of two kinds of paint, a consumer testing service finds that four 1-gallon cans of one brand cover on the average 546 square feet with a standard deviation of 31 square feet, whereas four 1-gallon cans of another brand cover on the average 492 square feet with a standard deviation of 26 square feet. Assuming that the two populations sampled are normal and have equal variances, test the null hypothesis μ₁ - μ₂ = 0 against the alternative hypothesis μ₁ - μ₂ > 0 at the 0.05 level of significance.