1. 15 eggs were weighed in order to estimate the spread of the weight of eggs delivered to the shop by an egg producer. The weights were the following: 62, 57, 70, 58, 59, 67, 65, 69, 55, 57, 60, 54, 72, 66, 74 g. What are the confidence interval for the average weight and for the spread of eggs’ weight at the confidence level 0.95?
2. The sodium content in thirty 300 gram boxes of organic corn flakes was determined. The data is 131.15, 130.69, 130.91, 129.54, 129.64, 128.77, 130.72, 128.33, 128.24, 129.65, 130.14, 129.29, 128.71, 129.00, 129.39, 130.42, 129.53, 130.12, 129.78, 130.92, 131.15, 130.69, 130.91, 129.54, 129.64, 128.77, 130.72, 128.33, 128.24 and 129.65 mg. Can you agree that the sodium content of this brand of cornflakes differs from 130 mg at ¿0.01
?
3. Two different test methods are used for determining the viscosity of synthetic rubber.
One method is used in the manufacturer’s laboratory and the other is used in the customer’s lab. Ten test samples were split with one part of the sample sent to each lab.
The following data were obtained:
Sample Manufacturer Customer
A 91.7 92.26
B 91.87 96.59
C 93 95.05
D 93.94 93.66
E 92.61 94.61
F 92.89 95.6
G 92.63 93.44
H 92.35 93.84
I 92.21 93.76
J 93.44 96.17
Does the manufacturer's laboratory provide the same value of rubber viscosity as the customer's laboratory?
4. There was examined the influence of temperature and catalyst on the yield of technological process. The results of experiment are shown in the table.
Temperature (◦C) Catalyst Yield (g)
160 C1 59, 61
160 C2 50, 54
160 C1 50, 58
160 C2 46, 44
180 C1 74, 70
180 C2 81, 85
Analyze the experimental data and tell whether these two factors have an influence on process yield or not.
5. Stack-losses of ammonia Y were measured in course of 21 days of operation of a plant for the oxidation of ammonia (NH3) to nitric acid (HNO3). The factors influencing stack losses were: the flow of cooling air x1 , the temperature of cooling water x2 , and acid concentration x3 . The experimental data is given in the table.
y 42 37 37 28 18 18 19 20 15 14 14 13 11 12 8 7 8 8 9 15 15
x180 80 75 62 62 62 62 62 58 58 58 58 58 58 50 50 50 50 50 56 70
x227 27 25 24 22 23 24 24 23 18 18 17 18 19 18 18 19 19 20 20 20
x389 88 90 87 87 87 93 93 87 80 89 88 82 93 89 86 72 79 80 82 91
Fit a multiple regression model to this data. Discuss the obtained results. Use the regression model to predict stack-loss of ammonia when x1=61 , x2=20 and x3=85 .
