A fertilizer mixing machine is set to give 4 kg of nitrate for every quintal bag of fertilizers. Five 100 kg bags are examined. The percentages of nitrate are: 2, 6, 4, 3, 1. is there reason to believe that the machine is defective?
x d=(x -x bar) (x -x bar)^2
2 -1.2 1.44
6 2.8 7.84
4 .8 0.64
3 0-.2 0.04
1 -2.2 4.84
d bar = 3.2
∑(x-d bar)^2 =14.8
sd = sqrt((14.8/4)) = 1.92
t = 3.72
p-value = 0 .9898
Degree of freedom = n -1 = 4
Since the computed value of t is less than the table value of t we accept and conclude that the population mean is 3.2
Well, with those percentages of nitrate, I think it's safe to say the fertilizer mixing machine missed the mark. It's either defective or it's under the impression that plants need a little extra "flavor" in their diet. Either way, it's not quite getting the job done!
To determine if there is a reason to believe that the machine is defective, we need to calculate the amount of nitrate expected from each bag and compare it to the actual amount provided.
Step 1: Calculate the expected amount of nitrate from each bag:
- The machine is set to give 4 kg of nitrate for every quintal bag (1 quintal = 100 kg).
- Therefore, for a 100 kg bag, we expect 4 kg of nitrate.
Step 2: Calculate the actual amount of nitrate from each bag:
- Multiply the percentage of nitrate by the weight of the bag in kg.
- For the five bags, the actual amounts of nitrate are:
- Bag 1: 2% * 100 kg = 2 kg
- Bag 2: 6% * 100 kg = 6 kg
- Bag 3: 4% * 100 kg = 4 kg
- Bag 4: 3% * 100 kg = 3 kg
- Bag 5: 1% * 100 kg = 1 kg
Step 3: Compare the expected and actual amounts of nitrate:
- Expected amount from each bag: 4 kg
- Actual amounts from the five bags:
- Bag 1: 2 kg
- Bag 2: 6 kg
- Bag 3: 4 kg
- Bag 4: 3 kg
- Bag 5: 1 kg
Step 4: Analyze the result:
- By comparing the expected amounts of 4 kg of nitrate to the actual amounts from the five bags, we can see that the actual amounts differ from the expected amounts.
- Since the machine is set to give 4 kg of nitrate for every quintal bag and the actual amounts of nitrate in the bags vary, it suggests that the machine might be defective.
Therefore, based on the given information, there is reason to believe that the fertilizer mixing machine is defective.
To determine if the fertilizer mixing machine is defective, we need to calculate the amount of nitrate that should be present in each bag based on the machine's settings and compare it to the actual percentages of nitrate found in the bags.
First, we need to convert the percentages of nitrate to kilograms. Since every quintal bag is 100 kg, we can calculate the amount of nitrate in each bag as follows:
Bag 1: (2/100) * 100 kg = 2 kg nitrate
Bag 2: (6/100) * 100 kg = 6 kg nitrate
Bag 3: (4/100) * 100 kg = 4 kg nitrate
Bag 4: (3/100) * 100 kg = 3 kg nitrate
Bag 5: (1/100) * 100 kg = 1 kg nitrate
Now let's compare the calculated amounts of nitrate with the desired amount of 4 kg.
Bag 1: 2 kg (less than 4 kg)
Bag 2: 6 kg (greater than 4 kg)
Bag 3: 4 kg (equal to 4 kg)
Bag 4: 3 kg (less than 4 kg)
Bag 5: 1 kg (less than 4 kg)
From the above comparison, we can see that only Bag 3 has the desired amount of 4 kg of nitrate. Bags 1, 4, and 5 have less nitrate than desired, while Bag 2 has more nitrate than desired.
Therefore, based on the results, there is reason to suspect that the fertilizer mixing machine is defective, as it is not consistently producing the desired amount of 4 kg of nitrate for every quintal bag of fertilizers.