1 Reading Contingency Tables The table below displays data concerning NYU STAT 2
ID: 3202709 • Letter: 1
Question
1 Reading Contingency Tables The table below displays data concerning NYU STAT 200 students in Spring 2017. Assume that the population of interest is all students who responded to the survey, unless otherwise specified. Use the following notation: • M = Male • W = Water
Tabulated Statistics: Biological Sex, Preferred Beverage:
Rows: Biological Sex Columns: Preferred Beverage
Beer Water wine Missing All
Female 25 184 74 1 283
Male 62 124 31 0 217
All 87 308 105 * 500
Cell Contents: Count
a. Compute P(W). Be sure to show all work! b. Compute P(M). Be sure to show all work! c. Compute P(WC) (c its sqr to the W, on the top right hand corner of the W). Be sure to show all work! d. Compute P (W M). Be sure to show all work! e. Compute P (W M). Be sure to show all work! f. If you were to randomly select one Penn State student from this population, what is the probability that the student is a female that prefers beer? Be sure to show all work! g. Given that a randomly selected student is prefers water, what is the probability that they are a male student? Be sure to show all work! Hint: How is this different from the probability in part f? i. Write this probability using statistical notation. ii. Find the probability. h. Given that a randomly selected student is a female, what is the probability that she does not prefer water? Be sure to show all work! Be sure to show all work! i. Write this probability using statistical notation. ii. Find the probability. i. Using the formulas from the online notes, check if the events M and W are independent. Be sure to show all work! j. Are M and W disjoint events? Why or why not?
Explanation / Answer
a)as total number of water taking people =308
and total number of people =500
hence P(W) =308/500
b) P(M) =total number of males/total number of people =217/500
c)P(Wc) =total number of people not taking water/total number of people =(500-308)/500=192/500
d)P(WnM) =total numbner of people taking water and are male/total number of people=124/500
e)P(WUM) =total numbner of people taking water or male/total number of people =(308+62+31)/500 =401/500
f))probability that the student is a female that prefers beer =P(FnB) =25/500
g)Given that a randomly selected student is prefers water,probability that they are a male student =P(M|W)
=P(MnW)/P(W) =(124/500)/(308/500) =124/308
h)it is different cause it is conditional probabilty where one event is considered that it has already happened.
i)
P(M|W) =P(MnW)/P(W)=(124/500)/(308/500) =124/308
h)Given that a randomly selected student is a female, probability that she does not prefer water =(283-184)/283
=99/283
i) P(Wc|F) =P(FnWc)/P(F) =(283-184)/500/(283/500) =99/283
here P(MnW) =124/500
and P(M)*P(W) =217/500 *308/500
as P(MnW) is not equal to P(M)*P(W) they are not independent
for them to be disjoint P(MnW) should be equal to 0 which is not. hence they are not disjoint
beer water wine total female 25 184 74 283 male 62 124 31 217 total 87 308 105 500Related Questions
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