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Katrina owns a sandwich shop. She wants to know if she can sell more chicken sandwiches if they are prepared with a special sauce. Katrina sells regular chicken sandwiches on a random sample of 10 days and she sells sandwiches with the special sauce on a random sample of 10 days. She collects data on the number of sandwiches sold each day.

Regular sandwiches: 15, 17, 22, 22, 25, 15, 18, 20, 25, 24
Special sauce: 18, 20, 35, 28, 18, 20, 20, 30, 24, 35

The means are 20.3 and 24.8 respectively, for a difference of 4.5. Katrina wants to know if this is significant or if it could be caused by chance. To find out, she re-randomizes the results 15 times and finds the differences of the means. The dot plot shows the data.

What is the best conclusion for Katrina to make based on the data?

A. The difference of 4.5 is significant because the re-randomizations show that it is outside the range of what could happen by chance.
B. The difference of 4.5 is significant because the re-randomizations show that it is within the range of what could happen by chance.
C. The difference of 4.5 is not significant because the re-randomizations show that it is outside the range of what could happen by chance.
D. The difference of 4.5 is not significant because the re-randomizations show that it is within the range of what could happen by chance.

Answer :

The difference of 4.5 is significant because the re-randomizations show that it is outside the range of what could happen by chance. This is the right answer>

Based on the provided information, Katrina observed a difference of 4.5 between the mean number of sandwiches sold with the special sauce compared to regular sandwiches. To determine if this difference is significant or could be due to chance, Katrina re-randomized the results 15 times and found the differences of the means.

The dot plot shows the distribution of these differences. Since the difference of 4.5 falls outside the range of what could happen by chance in the re-randomizations, Katrina can conclude that the difference is significant. Therefore, the best conclusion for Katrina to make based on the data is:

"The difference of 4.5 is significant because the re-randomizations show that it is outside the range of what could happen by chance."

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