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Air travel can be very frustrating when flights don't leave on time! Over the last $5\text{ months}$, $15\%$ of Be Free Airline flights were delayed. For the same time period, $20\%$ of Fly Me Away Airline flights were delayed.

In the process of investigating the difference between the two airlines, a consumer's group randomly selects $80\text{ flights}$ from each company during this time period and finds the proportion of flights that were delayed for each. They calculate the standard deviation of the sampling distribution of the difference between these two proportions. Their calculations are shown below:

$${ \sigma }_{ { p }_{ B }-{ p }_{ F } }=\sqrt { \dfrac { (0.15)(0.85) }{ 80 } } +\sqrt { \dfrac { (0.20)(0.80) }{ 80 } } =0.085$$

Which of the following statements is true?


The calculation should use the delayed flight proportions from the two samples instead of the true proportions of delayed flights.


These two distributions should not be combined because they don't come from two independent samples.


The two samples should be combined into one large sample before computing the standard deviation.


The consumer organization added the standard deviation of the Be Free proportion to the standard deviation of the Fly Me Away proportion. Instead it should first add the variances from the two distributions, then take the square root:
${ \sigma }_{ { p }_{ B }-{ p }_{ F } }=\sqrt { \frac { (0.15)(0.85) }{ 80 } +\frac { (0.20)(0.80) }{ 80 } } =0.06$


The consumer's group calculated the standard deviation correctly.

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