QUESTION 2 In the first and second halves of the year, two measurements of refinery fuel-gas were taken every month and analysed for their hydrogen content (in percent). The first set of twelve measurements (sample 1; first half of the year) gave a mean value of 41.2 and s₁ = 5.2, while the second set (sample 2, 2nd half of the year) gave a mean value of 45.8 and s2 = 6.7. (a) Determine at the 0.05 level of significance, whether to accept or reject the null hypothesis that there is no difference (with regard to mean hydrogen content) between the refinery fuel-gas in the two halves of the year. (b) Test at the 90% certainty level, whether there is any reason to doubt the assumption that σ₁ = 02, as required for the two-sample t-test used in part (a). (c) Tackle this problem using Excel and the functions which have been introduced to you. Of course, you will end up with the same conclusions.