Consider the function f(x, y) = x2 + xy + y2 defined on the unit disc, namely, D = {(x, y)| x2 + y2 ≤ 1}. Use the method of Lagr
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<span>Area of the upper rectangle = x(16 - 6) = 10x </span>yd²<span>
Area of the bottom rectangle = 6(x + 6) = 6x + 36 </span>yd²<span>
Total area = 10x + 6x + 36 = 16x + 36 yd</span>²
Area of the bottom rectangle = 6(x + 6) = 6x + 36 </span>yd²<span>
Total area = 10x + 6x + 36 = 16x + 36 yd</span>²
Answer:
a)
b) We are uncertain
c) It will change significantly
Step-by-step explanation:
a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.
Since we assume that the variances are equal, we use the pooled variance given as
,
where .
The mean difference .
The confidence interval is
b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.
c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.