Optimization problem: what are the dimensions of the lightest open-top right circularcylindrical can that will hold a volume of
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Answer:
It can be concluded that at 5% significance level that there is no difference in the amount paid by chain A and chain B for the job under consideration
Step by Step Solution:
The given data are;
Chain A 4.25, 4.75, 3.80, 4.50, 3.90, 5.00, 4.00, 3.80
Chain B 4.60, 4.65, 3.85, 4.00, 4.80, 4.00, 4.50, 3.65
Using the functions of Microsoft Excel, we get;
The mean hourly rate for fast-food Chain A, = 4.25
The standard deviation hourly rate for fast-food Chain A, s₁ = 0.457478
The mean hourly rate for fast-food Chain B, = 4.25625
The standard deviation hourly rate for fast-food Chain B, s₂ = 0.429649
The significance level, α = 5%
The null hypothesis, H₀: =
The alternative hypothesis, Hₐ: ≠
The pooled variance, , is given as follows;
Therefore, we have;
The test statistic is given as follows;
Therefore, we have;
The degrees of freedom, df = n₁ + n₂ - 2 = 8 + 8 - 2 = 14
At 5% significance level, the critical t = 2.145
Therefore, given that the absolute value of the test statistic is less than the critical 't', we fail to reject the null hypothesis and it can be concluded that at 5% significance level that chain A pays the same as chain B for the job under consideration