the various stages of sleep for a large group of people were monitored in 30-sec

Question

the various stages of sleep for a large group of people were monitored in 30-second intervals, or "epochs For each epoch, sleep stage was In a shudy, categorized as Wake, REM, or Non-REM. The accompanying table provides a summary of the results. Each cell of the table gives the number of epochs that occurred when transitioning from the previous sleep stage to the current sleep stage. Complede parts a through e below E Click the icon to view the sleep stage data table e. Are the events (previous stage is REM) and (ourrent stage is Non-REM) independent? Select the correct choice below and ill in the answer boxjes) to complete your choice Type an integer or a decimal. Round to three decimal places as needed) O A. Yes, because Pliprevious stage is REM) I (current stage is Non-REM)and Piprevious stage is REM OB. Yes becase Pturrent stage is Non-REMI "previous stage .s REM»-and P previous stage is REM) O C. No, because Pilcurent stage is Non-REM) 1(previous stage is REM) and Piprevious stage is REM) OD. No.because Puprevous sage is REM) lfarent stage s Non-REM)-and Ppronous stage is REM). Cick to select and enter your ansaerts) and then click Check Answer All parts showing Clear Al 2 6 8 0 Q W E R T Y U G H J

Explanation / Answer

Part (a), (b) and (c) are correct.

I am doing part (e) here

We have to find that are events (previous stage is REM) and (current stage non- REM) are independent ?

If both events are independent then

Pr(Previous stage is REM) * Pr( Current stage non- ERM) = Pr( Previous stage is REM and Current stage is non-ERM)

=> Pr(Previous stage is REM l Current stage is non- REM) = Pr( Previous stage is REM)

so Pr( Previous stage is REM l Current stage is non- REM) = 156/ (31268 + 156 + 1838) = 0.0047

Pr(Previous stage is REM) = 8353/ (33277 + 8353 + 7542) = 0.170

so these two doesn't match each other so these two events are not -independent.

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