During a four-day period, a height measurement and a weight measurement were recorded shortly after delivery for each baby born...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

1. There is a clear positive correlation between newborn length and weight: longer babies tend to weigh more.
2. Both groups (A and B) are represented throughout the length and weight ranges, with both present under \(3.5\text{ kg}\), indicating no obvious separation between groups by weight.
3. The length \(45-55\text{ cm}\) and weight \(2.5-4.5\text{ kg}\) ranges are typical for newborns, reflecting a normal population.
4. The groups appear roughly balanced in size, each containing about half of the 19 total babies.

Step-by-Step Solution

Question 1: Correlation Between Length and Weight

Complete Statement:

The correlation between length and weight for the babies in the study is _____

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: correlation between length and weight
    Meaning: This refers to how two variables (length and weight) are related—whether, as one increases, the other also increases, decreases, or doesn't follow any pattern.
    Relation to Chart: We must look at all babies' plotted points to see if, moving from left to right, the points go upward (positive), downward (negative), or scatter with no pattern (negligible).
    Important Implications: Recognizing the direction (if any) in the data's overall pattern lets us pick the correct qualitative label from the options.
• Statement Breakdown 2:
  • Key Phrase: for the babies in the study
    Meaning: Considers every individual in the dataset, regardless of subgroup.
    Relation to Chart: Count and consider all Group A (circles) and Group B (triangles) babies together.
    Important Implications: Don't split the dataset; judge the pattern by including both groups.

What is needed: Whether the combined data for all 19 babies shows a strongly positive, negligible, or strongly negative correlation between length and weight.

Solution:

• Condensed Solution Implementation:
  Scan the chart; if the plotted points generally increase together, the correlation is strongly positive. If there's no clear trend, it is negligible. If one increases as the other decreases, it is strongly negative.
• Necessary Data points:
  The relative positions of all 19 babies plotted by length (x-axis) and weight (y-axis). The trend formed by all these points.
  • Calculations Estimations:
    Visually, the babies' points move from lower left (shorter, lighter) to upper right (longer, heavier), clustering along an upward-sloping direction.
  • Comparison to Answer Choices:
    Only 'strongly positive' matches an overall clear upward trend. 'Negligible' would mean no trend; 'strongly negative' would require an obvious decline.

FINAL ANSWER Blank 1: strongly positive

Question 2: Probability of Group A Baby Under 3.5 kg

Complete Statement:

If a baby with weight less than \(3.5\text{ kg}\) were selected at random, the probability that the baby would be a part of Group A is _____

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: baby with weight less than \(3.5\text{ kg}\)
    Meaning: Focus only on babies whose weight is below \(3.5\text{ kg}\).
    Relation to Chart: Locate all circles and triangles that fall below the \(3.5\text{ kg}\) level on the y-axis.
• Statement Breakdown 2:
  • Key Phrase: selected at random
    Meaning: Each baby in this sub-group has equal probability of being chosen.
    Relation to Chart: We just count babies, not worry about their position beyond the weight filter.

What is needed: The exact fraction of babies below \(3.5\text{ kg}\) who are in Group A (number of Group A babies under \(3.5\text{ kg}\) ÷ total number of babies under \(3.5\text{ kg}\)).

Solution:

• Condensed Solution Implementation:
  Count the number of Group A (circle) and total babies below \(3.5\text{ kg}\). Divide: Group A count / total count.
• Necessary Data points:
  There are 2 Group A babies and 3 Group B babies under \(3.5\text{ kg}\), so 5 babies in total under \(3.5\text{ kg}\).
  • Calculations Estimations:
    Probability = \(\frac{2}{5} = 0.40\).
  • Comparison to Answer Choices:
    The answer set includes 0.33, 0.40, 0.44, 0.60, 0.67. Our math matches 0.40.

FINAL ANSWER Blank 2: 0.40

Summary

Question 1 is solved by visually judging the shape and trend of all data points, which clearly shows a strongly positive correlation. Question 2 simply counts Group A and all babies under the \(3.5\text{ kg}\) cutoff, giving a probability of \(0.40\). Both are straightforward when relating question wording to the chart.

Question Independence Analysis

The two questions are independent because the first involves qualitative assessment of the whole dataset's trend, while the second involves quantitative counting within a specific subset.