The designer of a new sheet metal stamping machine claims that their new machine can turn out a certain product faster than the machine now in use. Nine independent trials of stamping the same item on each machine gave the following results on times to completion:. Standard Machine: n1 = 9, x̄1 = 35.22 seconds, s1² = 24.4375 seconds² New Machine: n2 = 9, x̄2 = 31.56 seconds, s2² = 20.0275 seconds² Given the aforementioned data, the hypotheses H0: σ1² ≤ σ2² and H1: σ1² > σ2², and α = 0.05, is there evidence to conclude that σ1² ≤ σ2²? a. The test statistic equals 1.10, so there is evidence to conclude that σ1² ≤ σ2². b. The test statistic equals 0.91, so there is evidence to conclude that σ1² ≤ σ2². c. The test statistic equals 0.91, so there is not evidence to conclude that σ1² ≤ σ2². d. The test statistic equals 1.10, so there is not evidence to conclude that σ1² ≤ σ2². e. The test statistic equals 0.82, so there is not evidence to conclude that σ1² ≤ σ2². f. The test statistic equals 1.22, so there is not evidence to conclude that σ1² ≤ σ2². g. The test statistic equals 0.82, so there is evidence to conclude that σ1² ≤ σ2². h. The test statistic equals 1.22, so there is evidence to conclude that σ1² ≤ σ2².
The designer of a new sheet metal stamping machine claims that their new machine can turn out a certain product faster than the machine now in use. Nine independent trials of stamping the same item on each machine gave the following results on times to completion:.
Standard Machine: n1 = 9, x̄1 = 35.22 seconds, s1² = 24.4375 seconds²
New Machine: n2 = 9, x̄2 = 31.56 seconds, s2² = 20.0275 seconds²
Given the aforementioned data, the hypotheses H0: σ1² ≤ σ2² and H1: σ1² > σ2², and α = 0.05, is there evidence to conclude that σ1² ≤ σ2²?
| a. |
The test statistic equals 1.10, so there is evidence to conclude that σ1² ≤ σ2². |
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| b. |
The test statistic equals 0.91, so there is evidence to conclude that σ1² ≤ σ2². |
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| c. |
The test statistic equals 0.91, so there is not evidence to conclude that σ1² ≤ σ2². |
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| d. |
The test statistic equals 1.10, so there is not evidence to conclude that σ1² ≤ σ2². |
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| e. |
The test statistic equals 0.82, so there is not evidence to conclude that σ1² ≤ σ2². |
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| f. |
The test statistic equals 1.22, so there is not evidence to conclude that σ1² ≤ σ2². |
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| g. |
The test statistic equals 0.82, so there is evidence to conclude that σ1² ≤ σ2². |
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| h. |
The test statistic equals 1.22, so there is evidence to conclude that σ1² ≤ σ2². |
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