An industrial engineer collected data on the labor time required to produce an order of automobile mufflers using a heavy stamping machine. The data on times (hours) for n = 52 orders of different parts 2.15, 2.27, 0.99, 0.63, 2.45, 1.30, 2.63, 2.20, 0.99, 1.00, 1.05, 3.44, 0.49, 0.93, 2.52, 1.05, 1.39, 1.22, 3.17, 0.85, 1.18, 2.27, 1.52, 0.48, 1.33, 4.20, 1.37, 2.70, 0.63, 1.13, 3.81, 0.20, 1.08, 2.92, 2.87, 2.62, 1.03, 2.76, 0.97, 0.78, 4.68, 5.20, 1.90, 0.55, 1.00, 2.95, 0.45, 0.70, 2.43, 3.65, 4.55, 0.33, has 2424 39331 25 151 i=1 i=1 Assume that the population is normal. (a) What can one assert with 95% confidence about the maximum error if ē is used as a point estimate of the true population mean labor time required to run the heavy stamping machine? Construct a 95% confidence interval for the true population mean labor time. (b) Conduct a test of hypotheses with the intent of showing that the mean labor time is more than 1.5 hours at a = 0.05 significant level. What error could you have made? Explain in the context of the problem.

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An industrial engineer collected data on the labor time required to produce an
order of automobile mufflers using a heavy stamping machine. The data on times (hours)
for n = 52 orders of different parts
2.15,
2.27,
0.99,
0.63,
2.45,
1.30,
2.63,
2.20,
0.99,
1.00,
1.05,
3.44,
0.49,
0.93,
2.52,
1.05,
1.39,
1.22,
3.17,
0.85,
1.18,
2.27,
1.52,
0.48,
1.33,
4.20,
1.37,
2.70,
0.63,
1.13,
3.81,
0.20,
1.08,
2.92,
2.87,
2.62,
1.03,
2.76,
0.97,
0.78,
4.68,
5.20,
1.90,
0.55,
1.00,
2.95,
0.45,
0.70,
2.43,
3.65,
4.55,
0.33,
has
n
2424
39331
25
151
i=1
i=1
Assume that the population is normal.
(a) What can one assert with 95% confidence about the maximum error if ē
is used as a point estimate of the true population mean labor time required to run the
heavy stamping machine? Construct a 95% confidence interval for the true population
mean labor time.
(b) Conduct a test of hypotheses with the intent of showing that the mean
labor time is more than 1.5 hours at a = 0.05 significant level. What error could you
have made? Explain in the context of the problem.
Transcribed Image Text:An industrial engineer collected data on the labor time required to produce an order of automobile mufflers using a heavy stamping machine. The data on times (hours) for n = 52 orders of different parts 2.15, 2.27, 0.99, 0.63, 2.45, 1.30, 2.63, 2.20, 0.99, 1.00, 1.05, 3.44, 0.49, 0.93, 2.52, 1.05, 1.39, 1.22, 3.17, 0.85, 1.18, 2.27, 1.52, 0.48, 1.33, 4.20, 1.37, 2.70, 0.63, 1.13, 3.81, 0.20, 1.08, 2.92, 2.87, 2.62, 1.03, 2.76, 0.97, 0.78, 4.68, 5.20, 1.90, 0.55, 1.00, 2.95, 0.45, 0.70, 2.43, 3.65, 4.55, 0.33, has n 2424 39331 25 151 i=1 i=1 Assume that the population is normal. (a) What can one assert with 95% confidence about the maximum error if ē is used as a point estimate of the true population mean labor time required to run the heavy stamping machine? Construct a 95% confidence interval for the true population mean labor time. (b) Conduct a test of hypotheses with the intent of showing that the mean labor time is more than 1.5 hours at a = 0.05 significant level. What error could you have made? Explain in the context of the problem.
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