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 ? Can you agree that sodium content variation among boxes of organic corn flakes is smaller than 2 mg?
3. The acceleration of car was measured on two roads A and B, which have the same quality. Is it justified to claim that car acceleration is the same on both roads at the significance level of 0.01.
Measurement 1 2 3 4 5 6 7 8 9 10 11
acceleration on
road A [m/s2] 4.2 4.3 3.9 4.5 3.8 3.6 3.9 4.3 4.5 3.6 4.2 acceleration on
road B [m/s2] 4.8 5.2 4.2 5.1 4.7 4.3 4.9 5.3 5.6 5.2 4.8
4. Three groups of students, 5 in each group, were receiving therapy for severe test anxiety. Group 1 received 5 hours of therapy, group 2 - 10 hours and group 3 - 15 hours. At the end of therapy each subject completed an evaluation of test anxiety (the dependent variable in the study). Did the amount of therapy have an effect on the level of test anxiety?
Consider =0.01.
Group 1 - 5 hours Group 2 - 10 hours Group 3 - 15 hours
48 55 51
50 52 52
53 53 50
52 55 53
50 53 50
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. In model evaluation consider =0.02.
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 .