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 line plot shows the data.
What is the best conclusion for Katrina to make based on the data?
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.
The difference of 4.5 is significant because the re-randomizations show that it is within the range of what could happen by chance.
The difference of 4.5 is significant because the re-randomizations show that it is outside the range of what could happen by chance.
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.
my answer: C
Your answer is incorrect. The correct answer is A.
Explanation: In order to determine the significance of the difference between the means of the regular sandwiches and the sandwiches with special sauce, Katrina re-randomized the results 15 times. This is known as permutation testing or randomization testing.
By re-randomizing the results, Katrina is testing the null hypothesis that there is no difference between the two samples. If the observed difference of 4.5 is within the range of what could happen by chance, then this suggests that the difference is not significant and could be attributed to random variability.
However, if the observed difference of 4.5 is outside the range of what could happen by chance, then this suggests that the difference is significant and unlikely to be caused by random variability alone.
From the line plot, if the difference of 4.5 falls outside the range of the differences obtained from the re-randomizations, then Katrina can conclude that the difference is not significant and likely due to other factors such as the special sauce. Therefore, the correct conclusion for Katrina to make based on the data is that 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.