With reference to Example 4, for what values of ₁ - ₂ would the null hypothesis have been rejected ? Also find the probabilities of type II errors with the given criterion if

Example 4

An experiment is performed to determine whether the average nicotine content of one kind of cigarette exceeds that of another kind by 0.20 milligram. If n₁ = 50 cigarettes of the first kind had an average nicotine content of ₁= 2.61 milligrams with a standard deviation of s₁ = 0.12 milligram, whereas n₂ = 40 cigarettes of the other kind had an average nicotine content of x₂ = 2.38 milligrams with a standard deviation of s₂ = 0.14 milligram, test the null hypothesis μ₁ - μ₂ = 0.20 against the alternative hypothesis μ₁ - μ₂  0.20 at the 0.05 level of significance. Base the decision on the P-value corresponding to the value of the appropriate test statistic.