Question

Problem Scenario: Following is a problem description. For all hypothesis tests, you MUST state the statistical test you are using and use the P-VALUE METHOD through Microsoft Excel to make your decision. Show all steps, calculations, and work. For confidence intervals there is a specific Excel tool for each interval.  Treat each part of the question as a separate problem -- we use the same data set but are answering different “research questions”.

Many parts of cars are mechanically tested to be certain that they do not fail prematurely. In an experiment to determine which one of two types of metal alloy produces superior door hinges, 40 of each type were tested until they failed. To evaluate how long hinges made with the different alloys would last, the number of openings and closings was observed and recorded (to the closest 0.1 million). Car manufacturers consider any hinge that does not survive 1 million openings and closings to be a failure., A statistician has determined that the number of openings and closings is normally distributed.

NOTE: use ONLY the P-value method for hypothesis tests.

Number of Openings and Closings

Alloy 1				Alloy 2
1.5	1.5	0.9	1.3	1.4	0.9	1.3	0.8
1.8	1.6	1.3	1.5	1.3	1.3	0.9	1.4
1.6	1.2	1.2	1.8	0.7	1.2	1.1	0.9
1.3	0.9	1.5	1.6	1.2	0.8	1.2	1.1
1.2	1.3	1.4	1.4	0.8	0.7	1.1	1.4
1.1	1.5	1.1	1.5	1.1	1.4	0.8	0.8
1.3	0.8	0.8	1.1	1.3	1.1	1.5	0.9
1.1	1.6	1.6	1.3	1.4	1.2	1.3	1.6
0.9	1.4	1.7	0.9	0.6	0.9	1.8	1.4
1.1	1.3	1.9	1.3	1.5	0.8	1.6	1.3

a.) Estimate with 90% confidence the difference in the number of openings and closings between hinges made with Alloy1 and hinges made with Alloy 2. Interpret the interval.

b.) The quality control manager is not only concerned about the openings and closings of the hinges but is also concerned about the proportion of hinges that fail. Can we infer at the 10% significance level that the proportion of hinges made with Alloy 2 that fail exceeds 18%?

Answer 1

Alloy1		Alloy2
Mean	1.3275	Mean	1.145
Standard Error	0.044432	Standard Error	0.046403
Median	1.3	Median	1.2
Mode	1.3	Mode	1.4
Standard Deviation	0.281012	Standard Deviation	0.293476
Sample Variance	0.078968	Sample Variance	0.086128
Kurtosis	-0.55007	Kurtosis	-0.82585
Skewness	-0.10693	Skewness	0.024442
Range	1.1	Range	1.2
Minimum	0.8	Minimum	0.6
Maximum	1.9	Maximum	1.8
Sum	53.1	Sum	45.8
Count	40	Count	40

b)

No, we cannot infer at the 10% significance level that the proportion of hinges made with Alloy 2 that fail exceeds 18%?