The following data is on the completion time of a machining task taken by a random sample of 12 trainees and a random sample of 15 professional machinists (independent samples): Completion times (in minutes) 37 17 38 41 | 45 45 Trainees (X) 32 43 27 43 41 35 | 26 21 32 27 32 | 28 21 30 40 24 28 32 39 33 Professional 30 | 40 machinists (Y) Let µ, and µ, be the corresponding population mean completion times, and assume that the populations from which these completion times were sampled are normally distributed. 1- Are the professional machinists faster on the average than the trainees (µ, > µz) at the 1% level of significance? Test this by the following 5 steps. Step 1. Hypotheses and significance level: Но: Hạ: a = Step 2. Test Statistic and its sampling distribution under Ho: Step 3. Observed value of the test statistic: Step 4. P-value under Ho: Step 5. Decision and conclusion (interpretation of the result): 2- Construct a 99% confidence interval for µ,-µ2.

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The following data is on the completion time of a machining task taken by a random sample
of 12 trainees and a random sample of 15 professional machinists (independent samples):
Completion times (in minutes)
45 45
Trainees (X)
Professional
32 43 27 43|
41 37
17 38 41
35
26 21
32 27 32 22 28 21
30 | 40 24
28 32
39
33
machinists (Y)
Let µ, and u, be the corresponding population mean completion times, and assume that the
populations from which these completion times were sampled are normally distributed.
1- Are the professional machinists faster on the average than the trainees (u, > µ,)
at the 1% level of significance? Test this by the following 5 steps.
Step 1. Hypotheses and significance level:
Но:
На:
a =
Step 2. Test Statistic and its sampling distribution under Ho:
Step 3. Observed value of the test statistic:
Step 4. P-value under Ho:
Step 5. Decision and conclusion (interpretation of the result):
2- Construct a 99% confidence interval for H;-H2.
Transcribed Image Text:The following data is on the completion time of a machining task taken by a random sample of 12 trainees and a random sample of 15 professional machinists (independent samples): Completion times (in minutes) 45 45 Trainees (X) Professional 32 43 27 43| 41 37 17 38 41 35 26 21 32 27 32 22 28 21 30 | 40 24 28 32 39 33 machinists (Y) Let µ, and u, be the corresponding population mean completion times, and assume that the populations from which these completion times were sampled are normally distributed. 1- Are the professional machinists faster on the average than the trainees (u, > µ,) at the 1% level of significance? Test this by the following 5 steps. Step 1. Hypotheses and significance level: Но: На: a = Step 2. Test Statistic and its sampling distribution under Ho: Step 3. Observed value of the test statistic: Step 4. P-value under Ho: Step 5. Decision and conclusion (interpretation of the result): 2- Construct a 99% confidence interval for H;-H2.
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