Question
Three scientists want to estimate the mean weight of fish in the same lake.
To do this, each scientist randomly chose fish from the lake and recorded their weights. The samples are shown in the table.
(a)Fill in the sample means in the table.
Do not round your answers.
Sample Weight (in pounds) Sample mean
, , ,
, , ,
, , ,
(b)Use the table to calculate the range of the sample means.
(c)The scientists are going to use the sample means to estimate the mean weight of the fish in the lake.
Select all the true statements below.
The closer the range of the sample means is to , the more confident they can be in their estimate.
The farther the range of the sample means is from , the more confident they can be in their estimate.
The mean of the sample means will tend to be a better estimate than a single sample mean.
A single sample mean will tend to be a better estimate than the mean of the sample means.
To do this, each scientist randomly chose fish from the lake and recorded their weights. The samples are shown in the table.
(a)Fill in the sample means in the table.
Do not round your answers.
Sample Weight (in pounds) Sample mean
, , ,
, , ,
, , ,
(b)Use the table to calculate the range of the sample means.
(c)The scientists are going to use the sample means to estimate the mean weight of the fish in the lake.
Select all the true statements below.
The closer the range of the sample means is to , the more confident they can be in their estimate.
The farther the range of the sample means is from , the more confident they can be in their estimate.
The mean of the sample means will tend to be a better estimate than a single sample mean.
A single sample mean will tend to be a better estimate than the mean of the sample means.
Answers
GPT-4o mini
To assist with your request, I'll need you to provide the actual weight samples from the table for each scientist. However, I can guide you through the steps to solve the tasks.
(a) **Finding Sample Means:**
1. **Calculate the Mean for Each Sample:**
- For each scientist's sample, add up all their weights and divide by the number of fish in that sample.
- The formula for the mean is:
\[
\text{Sample Mean} = \frac{\text{Sum of Weights}}{\text{Number of Fish}}
\]
2. **Fill in the Sample Means:**
- If you provide me with the weights for each sample, I can help compute the sample means.
(b) **Calculating the Range of Sample Means:**
1. **Determine the Range:**
- The range is calculated as the difference between the maximum sample mean and the minimum sample mean:
\[
\text{Range} = \text{Maximum Sample Mean} - \text{Minimum Sample Mean}
\]
(c) **True Statements:**
1. **Select Valid Statements:**
- **The closer the range of the sample means is to 0, the more confident they can be in their estimate.** - True. A smaller range indicates consistency among the sample means.
- **The farther the range of the sample means is from 0, the more confident they can be in their estimate.** - False. A larger range indicates more variability among the sample means, suggesting less confidence.
- **The mean of the sample means will tend to be a better estimate than a single sample mean.** - True. Averaging the means helps reduce variability and gives a more reliable estimate.
- **A single sample mean will tend to be a better estimate than the mean of the sample means.** - False. The mean of several sample means generally provides a more stable estimation of the population mean.
If you provide the weights, I can perform the calculations for part (a) as well!
(a) **Finding Sample Means:**
1. **Calculate the Mean for Each Sample:**
- For each scientist's sample, add up all their weights and divide by the number of fish in that sample.
- The formula for the mean is:
\[
\text{Sample Mean} = \frac{\text{Sum of Weights}}{\text{Number of Fish}}
\]
2. **Fill in the Sample Means:**
- If you provide me with the weights for each sample, I can help compute the sample means.
(b) **Calculating the Range of Sample Means:**
1. **Determine the Range:**
- The range is calculated as the difference between the maximum sample mean and the minimum sample mean:
\[
\text{Range} = \text{Maximum Sample Mean} - \text{Minimum Sample Mean}
\]
(c) **True Statements:**
1. **Select Valid Statements:**
- **The closer the range of the sample means is to 0, the more confident they can be in their estimate.** - True. A smaller range indicates consistency among the sample means.
- **The farther the range of the sample means is from 0, the more confident they can be in their estimate.** - False. A larger range indicates more variability among the sample means, suggesting less confidence.
- **The mean of the sample means will tend to be a better estimate than a single sample mean.** - True. Averaging the means helps reduce variability and gives a more reliable estimate.
- **A single sample mean will tend to be a better estimate than the mean of the sample means.** - False. The mean of several sample means generally provides a more stable estimation of the population mean.
If you provide the weights, I can perform the calculations for part (a) as well!