STAT 200 Week 6 Homework Problems
9.1.2
Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students
who took the biology exam 84,199 of them were female. In that same year, of the 211,693 students
who took the calculus AB exam 102,598 of them were female ("AP exam scores," 2013). Estimate the
difference in the proportion of female students taking the biology exam and female students taking the
calculus AB exam using a 90% confidence level.
n1=144,796 n2=211,693
p1=84199/144796 = 0.582 p2=102598/211693 = 0.485
q1=1-0.582 = 0.418 q1=1-0.485 = 0.515
zc = 1.645
E=1.645*sqrt[{(0.582*0.418)/144796}+{90.485*0.515)/211693}]
E= 0.0028
(0.582-0.485)-0.0028<p1-p2<(0.582-0.485)+0.0028
0.0942<p1-p2<0.998
There is a 90% chance that 0.0942<p1-p2<0.998 contains true difference in proportions.
9.1.5
Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger
urban areas over states that are mostly rural? In the state of Pennsylvania, a fairly urban state, there
are 245 eight year olds diagnosed with ASD out of 18,440 eight year olds evaluated. In the state of Utah,
a fairly rural state, there are 45 eight year olds diagnosed with ASD out of 2,123 eight year olds
evaluated ("Autism and developmental," 2008). Is there enough evidence to show that the proportion
of children diagnosed with ASD in Pennsylvania is more than the proportion in Utah? Test at the 1%
level.
n1=18,440 n2=2,123
x1=245 x2=45
p1=245/18440 = 0.013 p2=45/2123 = 0.021
q1=1-0.013 = 0.987 q1=1-0.021 = 0.979
p-= (245+45)/(18440+2123) = 0.014
q-=1-0.014 = 0.986
z={(0.013+0.021)-0}/sqrt[{(0.014*0.986)/18440}+{(0.014*0.986)/2123}]
z=12.760
, 9.2.3
All Fresh Seafood is a wholesale fish company based on the east coast of the U.S. Catalina Offshore
Products is a wholesale fish company based on the west coast of the U.S. Table #9.2.5 contains prices
from both companies for specific fish types ("Seafood online," 2013) ("Buy sushi grade," 2013). Do the
data provide enough evidence to show that a west coast fish wholesaler is more expensive than an east
coast wholesaler? Test at the 5% level.
Table #9.2.5: Wholesale Prices of Fish in Dollars
All Fresh Catalina
Seafood Offshore
Fish Prices Products Prices
Cod 19.99 17.99
Tilapi 6.00 13.99
Farmed Salmon 19.99 22.99
Organic Salmon 24.99 24.99
Grouper Fillet 29.99 19.99
Tuna 28.99 31.99
Swordfish 23.99 23.99
Sea Bass 32.99 23.99
Striped Bass 29.99 14.99
Catalina
Fish All Fresh Offshore
Seafood Products
Prices Prices d=x1-x2
Cod 19.99 17.99 2
Tilapi 6 13.99 -7.99
Farmed
Salmon 19.99 22.99 -3
Organic
Salmon 24.99 24.99 0
Grouper Fillet 29.99 19.99 10
Tuna 28.99 31.99 -3
Swordfish 23.99 23.99 0
Sea Bass 32.99 23.99 9
9.1.2
Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students
who took the biology exam 84,199 of them were female. In that same year, of the 211,693 students
who took the calculus AB exam 102,598 of them were female ("AP exam scores," 2013). Estimate the
difference in the proportion of female students taking the biology exam and female students taking the
calculus AB exam using a 90% confidence level.
n1=144,796 n2=211,693
p1=84199/144796 = 0.582 p2=102598/211693 = 0.485
q1=1-0.582 = 0.418 q1=1-0.485 = 0.515
zc = 1.645
E=1.645*sqrt[{(0.582*0.418)/144796}+{90.485*0.515)/211693}]
E= 0.0028
(0.582-0.485)-0.0028<p1-p2<(0.582-0.485)+0.0028
0.0942<p1-p2<0.998
There is a 90% chance that 0.0942<p1-p2<0.998 contains true difference in proportions.
9.1.5
Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger
urban areas over states that are mostly rural? In the state of Pennsylvania, a fairly urban state, there
are 245 eight year olds diagnosed with ASD out of 18,440 eight year olds evaluated. In the state of Utah,
a fairly rural state, there are 45 eight year olds diagnosed with ASD out of 2,123 eight year olds
evaluated ("Autism and developmental," 2008). Is there enough evidence to show that the proportion
of children diagnosed with ASD in Pennsylvania is more than the proportion in Utah? Test at the 1%
level.
n1=18,440 n2=2,123
x1=245 x2=45
p1=245/18440 = 0.013 p2=45/2123 = 0.021
q1=1-0.013 = 0.987 q1=1-0.021 = 0.979
p-= (245+45)/(18440+2123) = 0.014
q-=1-0.014 = 0.986
z={(0.013+0.021)-0}/sqrt[{(0.014*0.986)/18440}+{(0.014*0.986)/2123}]
z=12.760
, 9.2.3
All Fresh Seafood is a wholesale fish company based on the east coast of the U.S. Catalina Offshore
Products is a wholesale fish company based on the west coast of the U.S. Table #9.2.5 contains prices
from both companies for specific fish types ("Seafood online," 2013) ("Buy sushi grade," 2013). Do the
data provide enough evidence to show that a west coast fish wholesaler is more expensive than an east
coast wholesaler? Test at the 5% level.
Table #9.2.5: Wholesale Prices of Fish in Dollars
All Fresh Catalina
Seafood Offshore
Fish Prices Products Prices
Cod 19.99 17.99
Tilapi 6.00 13.99
Farmed Salmon 19.99 22.99
Organic Salmon 24.99 24.99
Grouper Fillet 29.99 19.99
Tuna 28.99 31.99
Swordfish 23.99 23.99
Sea Bass 32.99 23.99
Striped Bass 29.99 14.99
Catalina
Fish All Fresh Offshore
Seafood Products
Prices Prices d=x1-x2
Cod 19.99 17.99 2
Tilapi 6 13.99 -7.99
Farmed
Salmon 19.99 22.99 -3
Organic
Salmon 24.99 24.99 0
Grouper Fillet 29.99 19.99 10
Tuna 28.99 31.99 -3
Swordfish 23.99 23.99 0
Sea Bass 32.99 23.99 9
