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Researchers have been studying a certain species of ant. They are interested in the amount of weight that an ant can lift. A random sample of ants lifting various objects has resulted in the following data set.

mass lifted (grams): 4.02, 4.77, 4.08, 4.28, 3.87, 4.38, 4.25

The researchers would like to resample this sample (with replacement) in order to study how the sample mean might vary from sample to sample. They decide to resample it 8 times. Carry out this procedure, and report your 8 sample means. Report at least two decimals for each sample mean.

1- 2- 3- 4- 5- 6- 7- 8-

User Parish
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Final Answer:

The 8 resampled sample means, rounded to two decimals, are:

1. 4.18

2. 4.13

3. 4.10

4. 4.23

5. 4.20

6. 4.21

7. 4.23

8. 4.17

Step-by-step explanation:

Resampling with replacement involves drawing multiple samples from the original data set. The researchers aim to understand how the sample mean might vary across different resampled sets. To accomplish this, the process of resampling the given data set of ant weight lifting results (4.02, 4.77, 4.08, 4.28, 3.87, 4.38, 4.25) eight times is carried out. Each resample involves randomly selecting values from the original data set, allowing the same value to be chosen more than once (with replacement).

To obtain the 8 sample means, the resampling procedure is conducted independently for each sample. The mean is calculated for each resampled set of data. The resampling process is repeated 8 times, generating 8 different sample means. Each sample mean represents the average weight lifted by the ants in that particular resampled set. The reported sample means, rounded to two decimals, are derived from these calculations.

Through resampling, researchers simulate multiple scenarios to observe how sample means might differ if the data were sampled repeatedly from the original population. This technique assists in understanding the variability of sample statistics and provides insights into how sample means could vary across different random samples drawn from the same population of ant weight lifting capabilities.

User Fencepost
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