Susan owns a chocolate store. She sells her chocolate by the gram and needs to compare the weights of two chocolate batches. She randomly selects 100 pieces from each batch. The distrubition of both samples are normal.
Batch 1 - (Mean Weight) 56 grams
Standard Deviation - 6 grams
Batch 2 - (Mean Weight) 40 grams
Standard Deviation - 6 grams
Which statement is true?
A. Batch 1 has higher degree or variability than batch 2
B. Every chocolate in batch 1 is lighter than every chocolate in batch 2
C. The difference in mean weight show that the populations are different
D. The fact that the standard deviations are equal means these populations are about the same.
If you are not sure of the correct answer, try to eliminate the wrong alternatives.
A. since SDs are equal, no.
B. With SDs of 6, there seems to overlap. 56 - 2SD = 44. 40 + 2SD = 52.
D. Nope, means differ 2.67 SD.
Guess what that leaves us with?
To compare the weights of two chocolate batches, we can analyze the given information about the mean weight and standard deviation of each batch.
In this case, we are given that Batch 1 has a mean weight of 56 grams with a standard deviation of 6 grams, while Batch 2 has a mean weight of 40 grams with a standard deviation of 6 grams.
Now, let's analyze each statement to determine which one is true:
A. Batch 1 has higher degree of variability than Batch 2:
To compare the degree of variability, we can look at the standard deviations. In this case, both batches have the same standard deviation of 6 grams. Therefore, statement A is false.
B. Every chocolate in Batch 1 is lighter than every chocolate in Batch 2:
The mean weights of the two batches indicate that, on average, Batch 1 chocolates are heavier than Batch 2 chocolates. However, this does not imply that every chocolate in Batch 1 is lighter than every chocolate in Batch 2. Therefore, statement B is false.
C. The difference in mean weights shows that the populations are different:
Given that the mean weight of Batch 1 is 56 grams and the mean weight of Batch 2 is 40 grams, there is a clear difference in the mean weights of the two batches. This difference in means suggests that the populations are different. Therefore, statement C is true.
D. The fact that the standard deviations are equal means these populations are about the same:
This statement is incorrect because having equal standard deviations does not necessarily mean that the populations are about the same. The standard deviation represents the spread of data within each batch and does not provide information about the difference in mean weights. Therefore, statement D is false.
In conclusion, the correct statement is C. The difference in mean weight shows that the populations are different.