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: µ1 - µ2 ≤ 0 and H1: µ1 - µ2 > 0, α = 0.05, and assuming that the both machines have the same variance, is there evidence to substantiate the designer’s claim? a. The t test statistic equals 1.65, so there is sufficient evidence to substantiate the designer’s claim. b. The z test statistic equals 1.75, so there is insufficient evidence to substantiate the designer’s claim. c. The t test statistic equals 1.75, so there is sufficient evidence to substantiate the designer’s claim. d. The t test statistic equals 1.65, so there is insufficient evidence to substantiate the designer’s claim. e. The z test statistic equals 1.65, so there is sufficient evidence to substantiate the designer’s claim. f. The z test statistic equals 1.65, so there is insufficient evidence to substantiate the designer’s claim. g. The z test statistic equals 1.75, so there is sufficient evidence to substantiate the designer’s claim. h. The t test statistic equals 1.75, so there is insufficient evidence to substantiate the designer’s claim.
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: µ1 - µ2 ≤ 0 and H1: µ1 - µ2 > 0, α = 0.05, and assuming that the both machines have the same variance, is there evidence to substantiate the designer’s claim?
| a. |
The t test statistic equals 1.65, so there is sufficient evidence to substantiate the designer’s claim. |
|
| b. |
The z test statistic equals 1.75, so there is insufficient evidence to substantiate the designer’s claim. |
|
| c. |
The t test statistic equals 1.75, so there is sufficient evidence to substantiate the designer’s claim. |
|
| d. |
The t test statistic equals 1.65, so there is insufficient evidence to substantiate the designer’s claim. |
|
| e. |
The z test statistic equals 1.65, so there is sufficient evidence to substantiate the designer’s claim. |
|
| f. |
The z test statistic equals 1.65, so there is insufficient evidence to substantiate the designer’s claim. |
|
| g. |
The z test statistic equals 1.75, so there is sufficient evidence to substantiate the designer’s claim. |
|
| h. |
The t test statistic equals 1.75, so there is insufficient evidence to substantiate the designer’s claim. |
Step by step
Solved in 3 steps with 1 images
