Engineering Stats/Probability
1) Sony Manufactures Color Televisions at two plants and wanted to compare the proportions of filled orders of Color Televisions on time from the two plants. The first plant is located at in Tai Pi in Taiwan and the second one is located in Seoul, South Korea. Sony selected 1,000 orders at random from each plant and found that 798 orders were completed on time from the Tai Pi plant and only 631 orders were completed on time from the Seoul plant.
A) Does the data in this sample support the claim of that the proportion of filled orders from the Tai Pi plant is greater than the proportion of filled order from the Seoul Plant? Perform a Hypothesis test; list all the required 5 steps in order to answer this question. Do NOT use the P-- VAULE or the Confidence Interval as a rejection rule here.
B) Repeat the only three required steps to test the same Hypothesis as in part A but use ONLY the P--VALUE as a rejection rule here.
2) The engine camshafts of a Toyota Camry is a vital part and it must have the appropriate hardness to wear properly as it has repeated contact with the engine lifters. To harden the camshaft, Toyta used an existing heat treatment of the shafts and it is known from the old process the hardness depth has histroical data is normall distributed with a mean is 4.5 mm and a standard deviation is 0.47 mm. Toyota developed a new heating process to reduce the variations in the camshaft hardness depth and used it. Toyota took a random samole of 30 camshafts after heating them using the new heating process and found that the camshaft hardness depth mean and standard deviations to be
?? = 4.5 ???? and S = 0.297489 mm respectively.
A) Does the data support the objective of Toyota that the popluation variance of all camshafts has been reduced by using the new heating process? Perform a Hypothesis test; list all the required 5 steps in order to answer the question. DO NOT use the P--VALUE or the Confidence Interval as a rejection rule here.
B) Repeat only the three required steps to test the same Hypothesis as in part A but use ONLY the P--Value as a rejection rule at alpha = 0.01.
3) over a two weeks period Amazon Monitors how many visits to its web site come every day from two different search engines 1 and 2 respectively. The paired data is given to you in Table 1 below.
|
Day
|
Visits from search Engine 1
|
Visits from search Engine 2
|
|
Day 1
|
85,851
|
66,356
|
|
Day 2
|
78,942
|
63,941
|
|
Day 3
|
75,501
|
62,217
|
|
Day 4
|
63,412
|
63,127
|
|
Day 5
|
80,069
|
61,176
|
|
Day 6
|
73,136
|
42,367
|
|
Day 7
|
66,731
|
45,448
|
|
Day 8
|
74,831
|
75,751
|
|
Day 9
|
78,616
|
61,820
|
|
Day 10
|
80,672
|
53,597
|
|
Day 11
|
73,083
|
55,313
|
|
Day 12
|
75,744
|
58,149
|
|
Day 13
|
57,580
|
40,645
|
|
Day 14
|
61,014
|
50,897
|
A) Is there a statistical significant difference between the means of number of visits for the two types 1 and 2 of the search engines? DO NOT use the P--VALUE or the Confidence Interval as a rejection rule here. Show all the required 5 steps including the distribution plot in order to gain full credits.
B) Reapeat only the three required steps to test the same Hypothesis as in part A but use ONLY the Confidence Interval as rejection rule here.
4) Artifical leather used in manfacturing car seats is made from two different extrusion machines and we are investigating the breaking strength of the leather produced. Two random sample of size n1 = 15 and n2 = 17 are selected from the two machines and the sample means and sample Standard deviations were calculated to be ??1 = 8.73 and ??2 = 8.68, S1= 0.591608 and S2 = 0.632456 respectively. It is known that these two sample are drawn from two normally distributed popluation that have uneqal variances.
A) is there evidence to support the claim that the two machines produce artifical leather with different breaking strengths? Do not use the P-- Value or the Confidence Interval as rejection rule here. Show all the required 5 steps including the distribution plot in order to gain full credit.
B) Repeat only the three required steps to test the same Hypothesis as in part A but use ONLY the confidence interval as a rejection rule here.
5) in a forging factory the required weight of a forged transmission's must weight more than 20 LBs in order to be accepted and used in car assembly of the required transmission. The forged pans' weiights are known to have a normal distibution. A random sample of 10 pans were selected from the forging factory and found that its mean of pans' weights equal 21.4 LBs with a standard deviation equals to 2.1 LBs. Use α = 0.025.
A) does the data in this sample meet the requirements of the transmissions' pans to be used in this GM on? Perform a Hypothesis test; list all the required 5 steps in order to answer the question including the required normal plot. DO NOT used the P--VALUE test or the Confidence Interval as a rejection rule here.
B) Repeat only the three required steps to test the same Hypothesis as in part A but use ONLY the P--Value as a rejection rule.
6) The maintenance cost of fixing 3 HP motors is normally distrubited with a standrad deviation of $3. A sample of 25 of these 3 HP motors were chosen from the maintenance center located in NewYork and their mean maintenance cost was to be found $ 20. Alpha = 0.05.
A) Does the data in this sample support the claim of that the mean of repairs of fixing all 3 HP motors is different than $ 21 per hour? Perform a Hypothesis test; list all the required 5 steps in order to answer the question including the standard normal distribution plot. USE ONLY the Confidence Interval as rejection rule.
B) Repeat only the three required steps to test the same Hypothesis s in part A but use ONLY the P--Valule as a rejection rule hree and include the standard normal distribution plot.
C) If the actual mean of the population of hourly maintenance costs of fixing all 3 HP motors is equal to $ 23. Calculate the Type II error probability β for the information given in part A.
7) A test is performed on 20 specimens of PVC pipe and the sample average and standard deviation were obtained to be ?? = 1.121 ft--lb/in and S = 0.328 respectively. The popluation of PVC pipes is normally distrubited. Use α = 0.01.
A) does the data in this sample support the claim that the popluation variance of all pipes is equal to 0.17. Perform a Hypothesis test; list all the required 5 steps in order to answer this question including the required plot. DO NOT use the P--Value or the Confidence Interval as a rejection rule here.
B) Repeat only the three required steps to test the same Hypothesis in part A but use ONLY the Confidence Interval as a rejection rule.
8) The breaking Strength of artifical leather used in manufacturing car seats is known to be approximately normally distributed. The mean breaking strength of the artificial leather is required to be equal 100 psi in order to be used in the car seats. A random sample of nine specimen of artificial leather is tested and their average breaking strength is found to be equal to 100.6 psi. And their standard deviation to be equal to 2 PSI
A) Should the artificial leather be judged accpetable? Perform a Hypothesis test; list all the required 5 steps in order to answer this question including the required normal plot. DO NOT use the P--Value or the Confidence Interval as rejection rule here.
B) Repeat only the three required steps to test the same Hypothesis as in part A but use P--VALUE as rejection rule.
9) The average life of a certain type of gas compressor used in Fracking process is 10 years with a standard devation of 1 year. The lives of these compressors are normally distributed. The manufacturer; Ingersoll--Rand replaces free of cost all compressors that fail while under guarantee. Ingersoll--Rand is willing to replace 3% of all compressors sold. For how many years should Ingersoll-- Rand set the period of guarantee for this type of Compressors? Draw the required normal distribution plots here.
10) Article in IEEE clamied that one--half of all engineers will continue academic graduate studies beyond the B.S. degree, hence receiving either an M.S. or a Ph.D degree. A sample of 484 newly graduates with B.S. in engineering were colloected from a university records where 267 student said that they are planning to continue their graduate studies in engineering. Use α = 0.05.
A) Does this data in this sample support the claim of the IEEE article? Perform a Hypothesis test; list all the required 5 steps in order to answer this question including the required normal plot. ONLY use the P--Value as rejection rule here.