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.
P1 = 84199/144796 = 0.5815
P2 = 102598/211693 = 0.4847
n1=144796, n2=211693
90% confidence interval for difference in P1-P2
= (0.5815-0.4847) +/-1.645*sqrt ((0.5815*(1-0.5815)/144796) + (0.4847*(1-0.4847)/211693))
= 0.0968+/-0.0028
= (0.0941, 0.0996)
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.
The result is not statistically significant at alpha level 0.01. So, there is not enough evidence to show
that the proportion of children diagnosed with ASD in PA is more than the proportion in UT. See
attached.
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.
See Attached.
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
9.2.6
The British Department of Transportation studied to see if people avoid driving on Friday the 13 th. They
did a traffic count on a Friday and then again on a Friday the 13 th at the same two locations ("Friday the
13th," 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean
difference in traffic count between the 6th and the 13th using a 90% level.
Table #9.2.6: Traffic Count
Dates 6th 13th
1990, July 139246 138548
1990, July 134012 132908
1991, September 137055 136018
1991, September 133732 131843
1991, December 123552 121641
1991, December 121139 118723
1992, March 128293 125532
1992, March 124631 120249
1992, November 124609 122770
1992, November 117584 117263
With 90% confidence, the true mean difference in traffic count between the two days is between
1154.1 and 2517.5. See attached.
9.3.1
The income of males in each state of the United States, including the District of Columbia and
Puerto Rico, are given in table #9.3.3, and the income of females is given in table #9.3.4
("Median income of," 2013). Is there enough evidence to show that the mean income of males is
more than of females? Test at the 1% level.
Table #9.3.3: Data of Income for Males
$42,951 $52,379 $42,544 $37,488 $49,281 $50,987 $60,705
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.
P1 = 84199/144796 = 0.5815
P2 = 102598/211693 = 0.4847
n1=144796, n2=211693
90% confidence interval for difference in P1-P2
= (0.5815-0.4847) +/-1.645*sqrt ((0.5815*(1-0.5815)/144796) + (0.4847*(1-0.4847)/211693))
= 0.0968+/-0.0028
= (0.0941, 0.0996)
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.
The result is not statistically significant at alpha level 0.01. So, there is not enough evidence to show
that the proportion of children diagnosed with ASD in PA is more than the proportion in UT. See
attached.
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.
See Attached.
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
9.2.6
The British Department of Transportation studied to see if people avoid driving on Friday the 13 th. They
did a traffic count on a Friday and then again on a Friday the 13 th at the same two locations ("Friday the
13th," 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean
difference in traffic count between the 6th and the 13th using a 90% level.
Table #9.2.6: Traffic Count
Dates 6th 13th
1990, July 139246 138548
1990, July 134012 132908
1991, September 137055 136018
1991, September 133732 131843
1991, December 123552 121641
1991, December 121139 118723
1992, March 128293 125532
1992, March 124631 120249
1992, November 124609 122770
1992, November 117584 117263
With 90% confidence, the true mean difference in traffic count between the two days is between
1154.1 and 2517.5. See attached.
9.3.1
The income of males in each state of the United States, including the District of Columbia and
Puerto Rico, are given in table #9.3.3, and the income of females is given in table #9.3.4
("Median income of," 2013). Is there enough evidence to show that the mean income of males is
more than of females? Test at the 1% level.
Table #9.3.3: Data of Income for Males
$42,951 $52,379 $42,544 $37,488 $49,281 $50,987 $60,705
