Shift 1	Shift 2
92	91
107	102
104	90
109	102
104	98
91	106
104	94
101	104
95	91
90	95
99	108
107	92
110	94
105	101
96	96

a) The point estimate of the difference in the average production is ["-1.92533", "3.333333", "-1.73333", "2.8", "-.33521", "2.5899", "-1.46667", "0.933333"] .

b) The estimated standard error for the difference in means is ["2.24358", "2.356913", "1.04819", "2.070963", "2.116751", "2.22254", "2.10969", "2.297549"] .

c) To test the hypothesis that the mean production is the same for both shifts the relevant degrees of freedom for the test are ["27", "26", "28", "30", "29"] .

d) For a test of the null hypothesis that means production levels are the same for both shifts the test statistic is ["1.352028", "-0.77989", "-2.42762", "0.440927", "1.450822", "1.327209", "-.614382", "-0.65372"] .

e) The appropriate p-value for this test is ["0.195554", "0.441999", "0.116178", "0.656222", "0.157941", "0.187584", "0.662776", "0.043753", "0.518627"] .

f) Based on your results and using a 0.05 level of significance for your test you ["reject", "fail to reject"] the null hypothesis.

Now suppose instead that the company has long held that production on Shift 1 is at least a full unit more than that of Shift 2, on average. A recently promoted manager challenges this assumption and keeps records on output levels for 15 days to test this assumption; these are the same observations as below.

g) Under the new scenario the null hypothesis is ["the mean for shift 1 minus the mean for shift 2 is equal to 1.", "the mean for shift 1 minus the mean for shift 2 is less than 1.", "the mean for shift 1 minus the mean for shift 2 is greater than or equal to 1.", "the mean for shift 1 minus the mean for shift 2 is less than or equal to 1."] .

h) The test statistic for the new manager's test is ["-1.22982", "-1.42587", "1.678438", "0.869161", "0.853206", "-1.09943", "-0.03149", "1.015575"] .

i) Based on the test statistic the new manager ["fails to reject", "rejects"] the new null hypothesis.