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

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

NOTE: use ONLY the P-value method for hypothesistests.

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 differencein the number of openings and closings between hinges made withAlloy1 and hinges made with Alloy 2. Interpret the interval.

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