A restaurant asked a focus group to rate 5 new dishes, each of which features either beef, chicken, fish, pork,...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

Each row-column intersection in the matrix shows which of two dishes was preferred, providing a full set of pairwise preference data. However, there are some missing or inconsistent entries (e.g., no comparison between chicken and pork, and an error in the fish vs pork cell), so the dataset is slightly incomplete. Overall, no single dish dominated all others; preferences were distributed among the offerings, showing varied tastes among participants.

Step-by-Step Solution

Question 1: Most Preferred Dish

Complete Statement:

The focus group preferred the dish featuring [BLANK] to every other dish.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: preferred the dish featuring [BLANK] to every other dish
    Meaning: We are searching for a single dish that the group chose over all the other options in direct comparisons.
    Relation to Chart: We need to check which dish was selected as the winner in every one of its head-to-head matchups in the chart.
    Important Implications: The answer must be the only dish that beat all other dishes in the one-on-one preference comparisons.

• Statement Breakdown 2:
  • Key Phrase: every other dish
    Meaning: Includes all of the remaining dishes except the one being considered.
    Relation to Chart: Each dish will be compared to each of the other four dishes.
    Important Implications: We need a dish with 4 wins (since there are 5 dishes total).

• What is needed: Which dish won all its head-to-head preference contests.

Solution:

• Condensed Solution Implementation:
  Count each dish's wins in its head-to-head matchups from the chart. The dish with 4 wins is the most preferred.
• Necessary Data points:
  Total number of wins for each dish in the chart: Beef (1), Chicken (3), Fish (3), Pork (1), Tofu (4).
  • Calculations Estimations:
    Beef beats Pork only. Chicken beats Beef, Fish, Pork. Fish beats Beef, Chicken, Pork. Pork beats Tofu only. Tofu beats Beef, Chicken, Fish, Pork.
  • Comparison to Answer Choices:
    Only Tofu is shown to beat all other dishes, making it the answer.

FINAL ANSWER Blank 1: Tofu

Question 2: Least Preferred Dish

Complete Statement:

The focus group preferred every other dish to the dish featuring [BLANK].

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: preferred every other dish to
    Meaning: Looking for the dish that was rejected in favor of all others.
    Relation to Chart: Find the dish that lost in all or almost all comparisons.

• Statement Breakdown 2:
  • Key Phrase: the dish featuring [BLANK]
    Meaning: Refers to the specific dish we're trying to identify as least preferred.
    Relation to Chart: Check the head-to-head results for each dish to see which lost the most.

• What is needed: Which dish lost the most or all head-to-head preference contests.

Solution:

• Condensed Solution Implementation:
  Review the chart and identify which dish lost the most head-to-head contests.
• Necessary Data points:
  Beef (1 win, 3 losses), Chicken (3 wins, 1 loss), Fish (3 wins, 1 loss), Pork (1 win, 4 losses), Tofu (4 wins, 0 losses).
  • Calculations Estimations:
    Pork wins only against Tofu, losing to Beef, Chicken, Fish, and Tofu. Pork therefore has 4 losses.
  • Comparison to Answer Choices:
    Pork has the most losses, so it is the least preferred dish.

FINAL ANSWER Blank 2: Pork

Summary

By analyzing the chart and counting the number of wins for each dish, Tofu is the only dish to have 4 wins—making it the most preferred. Pork, with only 1 win and 4 losses, is least preferred. The questions require counting wins and losses for each dish in the preference matrix.

Question Independence Analysis

The blanks are independent: one asks which dish wins against all others, the other which dish loses to all others. Answering one does not give away the answer to the other.