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
... [Show More] 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.
X1 = number of female students who took biology exam X2 = number of female students who took AP exam
P1 = proportion of female students who took biology exam P2 = proportion of female students who took AP exam
Ho: P1 = P2
Ha: P1 > P2 or Ho: P1 – P2 = 0
Ha: P1 – P2 >0
a = 0.90
z = 56.86
p = 0 Therefore we can reject null hypothesis
There is a 90% chance that 0.0941 < P1 – P2 < 0.0996 contains the true difference in proportions
The proportion of female students who took biology test is 9.41% to 9.96% higher than the proportion of female students who took AP exam.
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.
X1 = number of children diagnosed with ASD in Pennsylvania X2 = number of children diagnosed with ASD Utah
P1 = proportion of children diagnosed with ASD in Pennsylvania P2 = proportion of children diagnosed with ASD in Utah
Ho: P1 = P2 or Ha: P1 – P2 = 0 Ha: P1 > P2 Ha: P1 – P2 >0
a = .01
z = -2.93
p = 0.998
Since p-value is greater than 0.01 we fail to reject the null hypothesis
There is not enough evidence to show that proportion of eight years old diagnosed with ASD in Pennsylvania is more than proportion 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
Fish All Fresh Seafood
Prices Catalina Offshore
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
X1 = price of fish in All Fresh Seafood
X2 = price of fish in Catalina Offshore Products U1 = mean price of fish in All Fresh Seafood
U2 = mean price of fish in Catalina Offshore Products H0: Ud = 0
Ha: Ud < 0 a = 0.05
t = 0.9915 p-value = 0.825
Since p-value is more than level of significance we reject null hypothesis and conclude that there is not sufficient evidence to support the claim that west coast fish wholesalers are more expensive than east cost wholesaler.
9.2.6
The British Department of Transportation studied to see if people avoid driving on Friday the 13th. They did a traffic count on a Friday and then again on a Friday the 13th 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
X1 = traffic count on 6th X2 = traffic count on 13th
U1 = mean traffic count on 6th U2 = mean traffic count on 13th H0: Ud = 0
Ha: Ud ≠ 0 a = 0.90
The confidence interval is (1154.1, 2517.5). Therefore, the mean differences in traffic counts between 1154.1 and 2517.5.
Therefore, there is 90% confidence that the true mean difference in traffic counts between Friday the 6th
and Friday the 13th is between 1154.1 and 2517.5. [Show Less]