3.6.90 Question Help a studythie vanous stages ot sleep for a large group of peo

Question

3.6.90 Question Help a studythie vanous stages ot sleep for a large group of people wero montored in 30-second intervals, or-epochs-For each epocn, sleep stage was tegorized as Wake, REM, or Non-REM. The accompanying table provides a summary of the resuits. Each cel of the table gives the number of epochs at occurred when transitioning from the previous sleep stage to the current sleep stage. Complete parts a through e below Cick the icon to view the sleep stage data table d. Are the e ts previous stage is wake) and (current stage is wake) independent? Select the corect cho ce beow and S n the ansar buaj complete your choice (Type an integer or a decimal. Round to three decimal places as needed.) . OA. No, because Pl(ourrent stage is Wake) 1 (previous stage is Wakoll sand Pieevious stage is Weke)a B. No, because P(previous stage is Wake)I(current stag! O Sleep Stage Data Table O D. Yes, because Pi(previous stage is Wake) (current stag Previous Sieep Stage Curent Stage Non REM REM e Click to select and enter your answerts) and then click Ched Non-REM 31 288 REM 373 7,891 otas 33277 353 7,542 PrtSc 3 8 0

Explanation / Answer

The events {previous stage is Wake} and {current stage is Wake} are independent if
P(previous stage is Wake | current stage is Wake) = P(previous stage is Wake)
or,
P(Current stage is Wake | Previous stage is Wake) = P(Current stage is Wake)

Total observations = 33277 + 8353 + 7542 = 49172
P(previous stage is Wake) = Number of Wake in Previous stage / Total Observations = 7542 / 49172 = 0.153
P(current stage is Wake) = Number of Wake in Current stage / Total Observations = (1636 + 306 + 5547) / 49172 = 0.152
P(current stage is Wake | previous stage is Wake) = Number of Wake in Current Stage which were in Previous stage/ Number of Wake in Previous stage
= 5547 / 7542 = 0.735
P(previous stage is Wake | current stage is Wake) = Number of Wake in Previous Stage which are in Current stage/ Number of Wake in Current stage
= 5547 / (1636 + 306 + 5547) = 0.741

So, the answer is (B),
No, because P(previous stage is Wake | current stage is Wake) = 0.741 and P(previous stage is Wake) = 0.153

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