Kiara Tilghman
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.
84199 =0.5815 102598 =0.4847 =(0.5815-0.4847) + 1.645
144796 211693 0.5815(1-0.5815) + 0.4847(1-0.4847) =0.0968 +
0.0028
144796 211693 =(0.094, 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.
Xl=245 p2= 45/ 2123= 0.021196
Pl= xl/ nl = 245/18440 = 0.0130 significant level= 0.01
n2= 2123 p (Pennsylvania)= 245/ 18440= 0.013286
x2= 45 p (Utah)= 45/ 2123= 0.021196
245 + 45 =0.014103 0.013286 – 0.021196 t= 2.92699
18440 + 2123 0.014103 * (1-0.014103)(1/ 18440 + 1/ 2123) p- value= 0.998
Fail to reject Ho, the result is not statistically significant at .01 level of significance. There isn’t enough
evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the
proportion of children diagnosed with ASD in Utah.
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
Given test is at 5%. Hence level of significant, a= 0.05% test statistic = 2.445556 =
0.9915 D=22.01 D2= 491.8401` n=9 7.3994/ 9
Average of differences= 2.445556 degrees of freedom= n-
1=8 Sample Standard Deviation= 491.8401- 22.01
9 = 7.3994
8
Since p-value is more
than level of
significance, hence we
fail to reject the null
hypothesis,
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.
84199 =0.5815 102598 =0.4847 =(0.5815-0.4847) + 1.645
144796 211693 0.5815(1-0.5815) + 0.4847(1-0.4847) =0.0968 +
0.0028
144796 211693 =(0.094, 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.
Xl=245 p2= 45/ 2123= 0.021196
Pl= xl/ nl = 245/18440 = 0.0130 significant level= 0.01
n2= 2123 p (Pennsylvania)= 245/ 18440= 0.013286
x2= 45 p (Utah)= 45/ 2123= 0.021196
245 + 45 =0.014103 0.013286 – 0.021196 t= 2.92699
18440 + 2123 0.014103 * (1-0.014103)(1/ 18440 + 1/ 2123) p- value= 0.998
Fail to reject Ho, the result is not statistically significant at .01 level of significance. There isn’t enough
evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the
proportion of children diagnosed with ASD in Utah.
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
Given test is at 5%. Hence level of significant, a= 0.05% test statistic = 2.445556 =
0.9915 D=22.01 D2= 491.8401` n=9 7.3994/ 9
Average of differences= 2.445556 degrees of freedom= n-
1=8 Sample Standard Deviation= 491.8401- 22.01
9 = 7.3994
8
Since p-value is more
than level of
significance, hence we
fail to reject the null
hypothesis,
