Andrey works at a call center, selling insurance over the phone. He usually starts his calls with "Hello!" but he thinks that starting with "Howdy!" might improve the prospects of a juicy sale.

He randomized his subsequent 500 calls between a treatment group and a control group. He used "Hello!" in each of the control group calls and "Howdy!" in each of the treatment group calls, and he kept track of the sale price he achieved in each call.

The results of the experiment showed that the mean sale price of the treatment group was $\$ 20$ more than the mean of the control group. To test whether the results could be explained by random chance, Andrey created the table below, which summarizes the results of 1000 re-randomizations of the data (with differences between means rounded to the nearest 10 dollars).

According to the simulations, what is the probability of the treatment group's mean being higher than the control group's mean by $\$ 20$ or more?
$\square$
Assume that if the probability you found is lower than $5 \%$, then the result should be considered significant.

What should we conclude regarding the experiment's result?
Choose 1 answer:
(A) The results suggest that "Howdy!" improves sales prospects over "Hello!".
(B) The results could be due to random chance and do not prove anything conclusively.
\begin{tabular}{cc}
Treatment group mean - Control group mean & Frequency \
\hline-50 & 7 \
-40 & 13 \
-30 & 65 \
-20 & 123 \
-10 & 189 \
0 & 233 \
10 & 159 \
20 & 125 \
30 & 67 \
40 & 14 \
50 & 5
\end{tabular}

Question

Andrey works at a call center, selling insurance over the phone. He usually starts his calls with "Hello!" but he thinks that starting with "Howdy!" might improve the prospects of a juicy sale.

He randomized his subsequent 500 calls between a treatment group and a control group. He used "Hello!" in each of the control group calls and "Howdy!" in each of the treatment group calls, and he kept track of the sale price he achieved in each call.

The results of the experiment showed that the mean sale price of the treatment group was $\$ 20$ more than the mean of the control group. To test whether the results could be explained by random chance, Andrey created the table below, which summarizes the results of 1000 re-randomizations of the data (with differences between means rounded to the nearest 10 dollars).

According to the simulations, what is the probability of the treatment group's mean being higher than the control group's mean by $\$ 20$ or more?
$\square$
Assume that if the probability you found is lower than $5 \%$, then the result should be considered significant.

What should we conclude regarding the experiment's result?
Choose 1 answer:
(A) The results suggest that "Howdy!" improves sales prospects over "Hello!".
(B) The results could be due to random chance and do not prove anything conclusively.
\begin{tabular}{cc} 
Treatment group mean - Control group mean & Frequency \
\hline-50 & 7 \
-40 & 13 \
-30 & 65 \
-20 & 123 \
-10 & 189 \
0 & 233 \
10 & 159 \
20 & 125 \
30 & 67 \
40 & 14 \
50 & 5
\end{tabular}

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the total number of simulations where the treatment group mean is $20 or more higher than the control group mean. ‖ ‖ step 2 ⋮ Add the frequencies for the differences of $20, $30, $40, and $50. ‖ ‖ step 3 ⋮ The sum is $125 + 67 + 14 + 5 = 211$. ‖ ‖ step 4 ⋮ Calculate the probability by dividing the sum from step 3 by the total number of simulations. ‖ ‖ step 5 ⋮ The probability is $\frac{211}{1000} = 0.211$. ‖ ‖ step 6 ⋮ Since the probability is higher than 5%, the result is not considered statistically significant. ‖ ∻1 Answer∻ ***B*** ∻Key Concept∻ ⚹Statistical Significance⚹ ∻Explanation∻ ⚹If the probability of an event occurring by random chance is less than 5%, the result is considered statistically significant. In this case, the probability is higher than 5%, so the result is not statistically significant.⚹◊What is the formula to calculate the probability of the treatment group's mean being higher than the control group's mean by $20 or more based on the given table?⍭ Generate me a similar question◊

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