A researcher for an advertising firm is investigating the preferences of consume
ID: 3205397 • Letter: A
Question
A researcher for an advertising firm is investigating the preferences of consumers for a number of potential types of cookware. He is trying to determine the reasons for purchasing the types of cookware that the company offers. He takes a simple random sample of consumers and has each one fill out a questionnaire. The table below summarizes his results by showing the frequencies in each category. (NOTE: You need to find the row and column totals first to answer the questions below.)
Customer Age Group
Stainless Single Pan (SSP)
Non-stick Single Pan
(NSSP)
Stainless Set
(SSet)
Non-stick Set
(NSSet)
Totals
20-29
36
48
72
59
30-39
21
12
34
45
40-49
19
15
23
26
50-59
44
25
11
10
Totals
Part I. (1 pt each) A customer is selected randomly from this survey. Based on the information in the table, compute the following probabilities about the customer. (Give your answer as a fraction AND as a decimal rounded to three places in the given spaces.)
P (Age 20 – 29 and Age 50 – 59) =____________ _____________
P (Age 30 – 39 and NSSP) =______________ _________________
P (Age < 50) =____________________ ________________
P (NSSP or SSet) =___________________ _______________
P (NSSet or 20-29) = _________________ __________________
Part II. (1 pt each) Based on the information in the table, compute the following probabilities. (Give your answer as a fraction AND as a decimal rounded to three places.)
P(SSP) =_____________ _______________
P(Age 30-39) = ________________ _______________
P(SSP | Age 30-39) =________________ _________________
P(Age 30-39 | SSP) =________________ _________________
P(Age 30-39 and SSP) = _________________ _________________
Part III. (2 pts) Use the results of Part II and either Multiplication Rule or Conditional Probabilities to determine whether the events “Customer Age Group” and “Stainless Single Pan– SSP” are independent or dependent events. Explain your response.
__________________________________________________________________________________________
__________________________________________________________________________________________
Customer Age Group
Stainless Single Pan (SSP)
Non-stick Single Pan
(NSSP)
Stainless Set
(SSet)
Non-stick Set
(NSSet)
Totals
20-29
36
48
72
59
30-39
21
12
34
45
40-49
19
15
23
26
50-59
44
25
11
10
Totals
Explanation / Answer
Customer Age Group Stainless Single Pan (SSP) Non-stick Single Pan (NSSP) Stainless Set (SSet) Non-stick Set (NSSet) Totals 20-29 36 48 72 59 215 30-39 21 12 34 45 112 40-49 19 15 23 26 83 50-59 44 25 11 10 90 Totals 120 100 140 140 500 Total number of customers = 500 P (Age 20 – 29 and Age 50 – 59) = = P(Age 20-29)*P(Age 50-59) = (215/500)*(90/500) = 19350/250000 = 0.077 P (Age 30 – 39 and NSSP) = = P(Age 30-39)*P(NSSP) = ( 112/500)*(100/500) = 11200/250000 = 0.044 P (Age < 50) = =(215+112+83)/500 = 410/500 = 0.820 P (NSSP or SSet) = = P(NSSP)+P(SSet) = (100/500) + (140/500) = 240/500 = 0.480 P (NSSet or 20-29) = = P(NSSet)+P(20-29) = (140/500) + (215/500) = 355/500 = 0.710 P(SSP) = =120/500 = 0.240 P(Age 30-39) = =112/500 = 0.224 P(SSP | Age 30-39) = =P(SSP and Age 30-39)/P(Age 30-39) = (21/500)/(112/500) = 21/112 = 0.187 P(Age 30-39 | SSP) = =P(Age 30-39 and SSP)/P(SSP) = (21/500)/(120/500) = 21/120 = 0.175 P(Age 30-39 and SSP) = =P(Age 30-39)*P(SSP) = (112/500)*(120/500) = 13440/250000 = 0.053Related Questions
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