An engineer working for a large agribusiness has developed two types of soll additives he calls Addi and Add2. The engineer wants to rest whether there is any difference between the two additives in the mean yield of tomato plants grown using these additives The engineer studies a random sample of 12 tomato plants grown using Add1 and a random sample of 13 tomato plants grown using Add2(These samples are chosen independently.) The plants grown with Addi have a simple mean weld of 130.9 tomatoes with a sample variance of 105.4. The plants grown with Add2 have a sample mean yield of 168.3 tomatoes with a sample variance of 1256.9. Assume that the two populations of yields are approximately normally distributed. Can the engineer conclude, at the 0.01 level of significance, that there is a difference between the population mean of the yields of tomato plants grown with Add: and the population mean of the yields of tomato plants grown with Add22 Perform a two-tailed test. Then complete the parts below.

(a) State the null hypothesis H0 and the alternative hypothesis H₁.
(b) Determine the type of test statistic to use.
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.)