A fruit grower wants to test a new spray that a manufacturer claims will reduce the loss due to insect damage. To test the claim, the grower sprays 200 trees with the new spray and 200 other trees with the standard spray. The following data were recorded.
New Spray | Standard Spray | |
Mean Yield per Tree (lb) | 240 | 228 |
Variance s^{2} | 980 | 807 |
(a) Do the data provide sufficient evidence to conclude that the mean yield per tree treated with the new spray, μ_{1}, exceeds that for trees treated with the standard spray, μ_{2}? Use α = 0.05.
Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)
test statistic | z = |
rejection region | z > |
z < |
(b) Construct a 95% confidence interval for the difference
(μ_{1} − μ_{2}) between the mean
yields for the two sprays (in pounds). (Round your answers to two
decimal places.)
lb to lb
(a) Hypothesis: Vs
The test statistic is ,
The critical value is ,
Rejection region is ,
(b) The 95% confidence inetrval for the difference between the mean yield for the two sprays is ,
-42.88 lb to 66.88 lb
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