Malakai took 3 random samples of students at his middle school and asked for their heights. The data he collected is shown in the table below.

Question

PART A

Complete the last column of the table by finding the mean height of each sample.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Sample Heights (in feet) Sample Mean
1 4.9, 4.8, 5.1, 4.4, 5.3, 5.2 Response area
2 5.2, 5.4, 4.5, 4.7, 5.0, 4.3 Response area
3 4.2, 4.5, 5.0, 4.8, 4.7, 5.1 Response area


Question 2
PART B

Which of the following statements is true?

Responses
A The range of the sample means is
.The range of the sample means is 0 point 1 0.
B The average of the sample means, which is
, is a reasonable estimate for the average height of middle schoolers at Malakai's school.The average of the sample means, which is 4 point 8 4, is a reasonable estimate for the average height of middle schoolers at Malakai's school.
C If Malakai took smaller sample sizes, he would likely get sample means that are closer to the true mean.If Malakai took smaller sample sizes, he would likely get sample means that are closer to the true mean.
D The average of the sample means, which is
, is a reasonable estimate for the average height of middle schoolers at Malakai's school.The average of the sample means, which is 5 point 0, is a reasonable estimate for the average height of middle schoolers at Malakai's school.
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B

Answer 1

To complete the table with the mean heights for each sample, we can calculate the mean for each set of heights provided.

Mean Calculation:

1. Sample 1 Heights: 4.9, 4.8, 5.1, 4.4, 5.3, 5.2
   Mean = (4.9 + 4.8 + 5.1 + 4.4 + 5.3 + 5.2) / 6
   Mean = 29.7 / 6 = 4.95

2. Sample 2 Heights: 5.2, 5.4, 4.5, 4.7, 5.0, 4.3
   Mean = (5.2 + 5.4 + 4.5 + 4.7 + 5.0 + 4.3) / 6
   Mean = 29.1 / 6 = 4.85

3. Sample 3 Heights: 4.2, 4.5, 5.0, 4.8, 4.7, 5.1
   Mean = (4.2 + 4.5 + 5.0 + 4.8 + 4.7 + 5.1) / 6
   Mean = 28.3 / 6 = 4.71667 ≈ 4.72 (you can round to two decimal places)

Table Completion:

| Sample | Heights (in feet) | Sample Mean | |--------|---------------------------------------|-------------| | 1 | 4.9, 4.8, 5.1, 4.4, 5.3, 5.2 | 4.95 | | 2 | 5.2, 5.4, 4.5, 4.7, 5.0, 4.3 | 4.85 | | 3 | 4.2, 4.5, 5.0, 4.8, 4.7, 5.1 | 4.72 |

PART B:

To analyze the responses based on the sample means calculated:

The sample means are:

• Sample 1: 4.95
• Sample 2: 4.85
• Sample 3: 4.72

1. Range of Sample Means:
   Range = Max mean - Min mean = 4.95 - 4.72 = 0.23 (not 0.10).

2. Average of Sample Means:
   Average = (4.95 + 4.85 + 4.72) / 3 = 4.80667 ≈ 4.81. This means average is likely not 4.84 or 5.00.

3. If Malakai took smaller sample sizes: Typically, smaller sample sizes lead to more variability, so this statement is likely false.

Based on the above analyses, let's review the statements:

• A: False - The range is not 0.10.
• B: False - The average is closer to 4.8, but not exactly 4.84.
• C: False - Smaller samples would usually lead to more variability, resulting in means that could be farther from the true mean.
• D: False - The average calculated is not 5.0.

Conclusion:

None of the options A, B, C, or D seem to be correct as stated based on the calculations provided. If any option needs to be selected based on the closest values, you might consider option B regarding the average of the sample means, but it should be adjusted to reflect the actual average (which is close to 4.81).