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Engineering Probability and Inference Homework 1 On average, a certain pesticide contains 2% toxic material

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Engineering Probability and Inference Homework 1

1. On average, a certain pesticide contains 2% toxic material. Batches of the pesticide that contain too little or too much of the material cannot be approved for retail sale. In a random sample of 80 batches of the pesticide, the mean amount of toxic material was 1.93% with a standard deviation of 0.2% (or 0.0193 and 0.002). Do the data indicate that the mean amount of toxic material in the pesticide differs from 2%? Use a significance level of 5% for the hypothesis test AND a 95% confidence interval to justify your claim.

 

2. The Association of Oklahoma Independent Oil Producers would like to prove that the average production of Oklahoma oil wells is less than 24 barrels per day. The association randomly sampled seventeen actively pumping oil wells in the state. The sample produced a mean of 20.8 barrels per day and a standard deviation of 3.6 barrels. Use a 0.01 significance level to test the Associations claim.

 

3. If you would like to conduct a corresponding confidence interval for #2, what percent would it be? Find that confidence interval.

 

 

4. One approach to make green gasoline takes biomass in the form of sucrose and converts it into gasoline using catalytic reactions. At one step in a pilot plant process, a chemical engineer measures the output of carbon chains of length three. Nine runs with the same catalyst produced the following yields (in gallons): 0.63, 2.64, 1.85, 1.68, 1.19, 1.76, 0.83, 1.04, 0.68. Test the claim that the mean yield is greater than 1.2 gallons. Use α=0.05.

 

 

5. A researcher wants to know whether the acidity of rain near Houston, Texas is significantly different from that near Chicago, Illinois. He randomly selects 10 rain dates in Texas and 12 in Illinois and obtains the following:

Texas:    4.69    5.10      5.22      4.46      4.93      4.65      5.22      4.76       4.25             5.14     

Illinois:   4.40   4.69      4.22      4.64      4.54      4.35      4.69      4.40       4.75             4.93      4.45      4.49

Use a significance level of 5% to test the claim that there is a difference between the acidity rates. You can assume the population variances are equal and that the populations are normally distributed.

6. Using the information above, construct a 95% confidence interval for the difference between the two average rain amounts. Does your interval suggest there is a difference between the acidity rates? Why or why not? Does this answer agree with your answer in #5?

 

 

7. A civil engineer wants to compare two instruments for measuring the amount of polychlorinated biphenyls in corn stalks. A sample of 5 stalks is cut and crushed and two scoops of the material taken. One is measures with the first instrument and the other with the second instrument. Use α=0.05 to test if there is a mean difference in instrument readings.

Sample	1	2	3	4	5
Instrument 1	4	9	8	3	6
Instrument 2	5	7	6	5	4

 

 

8. In a study of the burn time of oak and pine, the following data was collected:
                

       Oak:              1.72    0.67    1.55    1.56    1.42    1.23    1.77  

       Pine:            0.98    1.40    1.33    1.52    0.73    1.20    1.48             

 

Use the Wilcoxon Rank Sum Test at a 0.05 level to test for a difference in true average burn time for the two types of wood.

 

 

9. The following are the weekly losses of worker-hours due to accidents in 10 plants before and after a safety program was put into operation. Use the Wilcoxon Signed-Rank Test and a significance level of 0.05 to test whether the safety program is effective.

 

Before	45	60	46	119	33	57	83	29	26	17
After	36	73	44	124	35	51	77	34	24	11