Math Problem Statement

Fat contents (x, in grams) for seven randomly selected frozen pizza brands that were among the brands receiving the highest ratings by a certain website are shown below. 9, 11, 10, 13, 10, 15, 8 The normal scores for a sample of size 7 are as follows. −1.364, −0.758, −0.353, 0, 0.353, 0.758, 1.364 Calculate the correlation coefficient for the (normal score, x) pairs. (Round your answer to four decimal places.)

Fat contents (x, in grams) for seven randomly selected frozen pizza brands that were among the brands receiving the highest ratings by a certain website are shown below. 9, 11, 10, 13, 10, 15, 8 The normal scores for a sample of size 7 are as follows. −1.364, −0.758, −0.353, 0, 0.353, 0.758, 1.364 Calculate the correlation coefficient for the (normal score, x) pairs. (Round your answer to four decimal places.)

Solution

The correlation coefficient for the (normal score, fat content) pairs is approximately 0.9682 (rounded to four decimal places). This indicates a strong positive correlation between the two variables.

Would you like more details on how this was calculated or the interpretation?

Here are 5 related questions to consider:

  1. How is the Pearson correlation coefficient used in statistics?
  2. Why does a correlation coefficient close to 1 indicate a strong relationship?
  3. What are normal scores, and how are they related to data distribution?
  4. How can you interpret negative correlation values compared to positive ones?
  5. What are some limitations of using Pearson correlation?

Tip: A correlation coefficient only measures linear relationships. Non-linear relationships require different methods.

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Math Problem Analysis

Mathematical Concepts

Correlation Coefficient
Statistics
Linear Relationship

Formulas

Pearson Correlation Coefficient: r = Σ[(x - mean_x)(y - mean_y)] / sqrt(Σ(x - mean_x)^2 * Σ(y - mean_y)^2)

Theorems

Pearson Correlation Coefficient

Suitable Grade Level

College or Upper High School

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