Questions: In a study of pain relievers, 20 people were given product A, and all but 6 experienced relief. In the same study, 100 people were given product B, and all but 37 experienced relief. Fill in the blanks below to make the most reasonable statement possible. Product performed better in the study. That is because only 66% failed to get relief with this product, whereas 70% failed to get relief with Product A ?

In a study of pain relievers, 20 people were given product A, and all but 6 experienced relief. In the same study, 100 people were given product B, and all but 37 experienced relief. Fill in the blanks below to make the most reasonable statement possible. Product performed better in the study. That is because only 66% failed to get relief with this product, whereas 70% failed to get relief with Product A ?
Transcript text: In a study of pain relievers, 20 people were given product A, and all but 6 experienced relief. In the same study, 100 people were given product B, and all but 37 experienced relief. Fill in the blanks below to make the most reasonable statement possible. Product $\square$ performed better in the study. That is because only $66 \%$ failed to get relief with this product, whereas $70 \%$ failed to get relief with Product $A$ $\square$ $?$ .
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Solution

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Solution Steps

Step 1: Identify the number of people who failed to get relief for each product
  • For Product A: 20 people were given the product, and all but 6 experienced relief. This means \( 20 - 6 = 14 \) people failed to get relief.
  • For Product B: 100 people were given the product, and all but 37 experienced relief. This means \( 100 - 37 = 63 \) people failed to get relief.
Step 2: Calculate the percentage of people who failed to get relief for each product
  • For Product A: The percentage of people who failed to get relief is \( \frac{14}{20} \times 100 = 70\% \).
  • For Product B: The percentage of people who failed to get relief is \( \frac{63}{100} \times 100 = 63\% \).
Step 3: Compare the percentages and fill in the blanks
  • Product B performed better in the study because only \( 63\% \) failed to get relief with this product, whereas \( 70\% \) failed to get relief with Product A.

Final Answer

Product \( B \) performed better in the study. That is because only \( 63\% \) failed to get relief with this product, whereas \( 70\% \) failed to get relief with Product \( A \).

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