Observation no Current state product weight (g) Product weight after using the new machine (g) 99 10 15 100 12 12 101 14 8 102 15 13 103 11 15 104 10 13 105 15 16 106 13 12 107 14 9 108 14 13 A company's quality engineer wants to check whether the average weight of the products coming out of the packaging line exceeds 10 grams. For this, he measured the weights of the products coming out of the line by making random selection. Measurement values are presented in the column "Current state product weight (g)". After a while, a pressing machine with a newer technology was replaced with a press machine where product losses were frequently experienced in the packaging line, and the products with the same features were weighed after being processed in this new pressing machine. The product weights obtained after the use of the new pressing machine are presented in the column "Product weight (g) after using the new machine". In line with these given, answer the following questions using the observation numbers that have been defined. a) Using the data set defined in the column "Current status product weight (gr)", test whether the average weight of the products currently exceeds 10 grams or not, at the level of a= 0.05 significance, write the relevant hypotheses and apply all necessary steps to make a decision. Write down the decision you made as a result of the hypothesis test and interpret your decision. b) The quality engineer of this company claims that after the use of the new machine, the average weight of the products coming out of the packaging line increases compared to the situation in which the old machine was used. Test this claim of the quality engineer at the significance level of a = 0.05 by writing the relevant hypotheses and applying all the necessary steps to make a decision. Write down the decision you made as a result of the hypothesis test and interpret your decision.
|
Observation no |
Current state product weight (g) |
Product weight after using the new machine (g) |
|
99 |
10 |
15 |
|
100 |
12 |
12 |
|
101 |
14 |
8 |
|
102 |
15 |
13 |
|
103 |
11 |
15 |
|
104 |
10 |
13 |
|
105 |
15 |
16 |
|
106 |
13 |
12 |
|
107 |
14 |
9 |
|
108 |
14 |
13 |
A company's quality engineer wants to check whether the average weight of the products coming out of the packaging line exceeds 10 grams. For this, he measured the weights of the products coming out of the line by making random selection. Measurement values are presented in the column "Current state product weight (g)". After a while, a pressing machine with a newer technology was replaced with a press machine where product losses were frequently experienced in the packaging line, and the products with the same features were weighed after being processed in this new pressing machine. The product weights obtained after the use of the new pressing machine are presented in the column "Product weight (g) after using the new machine". In line with these given, answer the following questions using the observation numbers that have been defined.
a) Using the data set defined in the column "Current status product weight (gr)", test whether the average weight of the products currently exceeds 10 grams or not, at the level of a= 0.05 significance, write the relevant hypotheses and apply all necessary steps to make a decision. Write down the decision you made as a result of the hypothesis test and interpret your decision.
b) The quality engineer of this company claims that after the use of the new machine, the average weight of the products coming out of the packaging line increases compared to the situation in which the old machine was used. Test this claim of the quality engineer at the significance level of a = 0.05 by writing the relevant hypotheses and applying all the necessary steps to make a decision. Write down the decision you made as a result of the hypothesis test and interpret your decision.
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