With an ever-increasing world population, grain yields are extremely important. A random sample of 16 large grain producing regions in the world gave the following information about grain production (in kg/hectare)

Does this information indicate that modern grain production is higher? Use a 5% level of significance.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Compute the sample test statistic. What is the sampling distribution?
(c) Find the P-value of the sample test statistic.
(d) Conclude the test.
(e) Interpret the conclusion in the context of the application.

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Region Modern Production 1610 2230 5270 6990 2010 4560 780 6510 Historic Production1590 2360 5161 7170 1920 4760 660 6320 外 6 7 Region Modern Production 2850 3550 710 2050 2750 2550 6750 3670 Historic Production 2920 2440 1340 2180 3110 2070 7330 2980 9 10 1 31415 16