STAT 200 Week 6 Homework Problems, full solution guide, 100% correct.

STAT 200 Week 6 Homework Problems Rubric Correct Answers with no work shown or partial work shown to justify the answer is graded at 50%. 1. Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology exam 84,000 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 99% confidence level. Answer: P 1=84000/=0.5815 P 2=/=0.4846 n1 =, n2= 99% confidence interval for difference in p1-p2 =(0.5815-0.4846)+/-1.645*sqrt((0.5815*(1-0.5815)/)+(0.4846*(1-0.4846)/)) =0.0968+/-0.0028 =(0.0941, 0.0996) 2. 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. Answer: n1=18,440 x1=245 p1=245/18440 = 0.013 q1=1-0.013 = 0.987 n2=2,123 x2=45 p2=45/2123 = 0.021 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 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 Answer X = 216.92 / 9 = 24.10 Y = 194.91 / 9 = 21.66 S1 = 534.3 / 8 = 66 .82 S2 = 250.00 / 8 = 31.25 T = 924.10- 21.66) / √ ((66.82 / 8 ) – 31.25 / 8)) = 2.44/2.11 = 1.16 Test Statistic: t = 2.45 / (7.39/√9) = 0.995 P value: 0.825 P value is less than test statistic There is enough evidence to conclude that West Coast wholesale is more expensive then the East Coast 4. 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 1990, July 1991, September 1991, September 1991, December 1991, December 1992, March 1992, March 1992, November 1992, November Answer: Mean= 1835.8 Standard Dev= 1173.065 df= 9 tc= 1.833 E= 679.962 There is a 90% chance that 2515.762ud2515.762 contains true mean difference between the 6th and the 13th 5. 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 $50,411 $66,760 $40,951 $43,902 $45,494 $41,528 $50,746 $45,183 $43,624 $43,993 $41,612 $46,313 $43,944 $56,708 $60,264 $50,053 $50,580 $40,202 $43,146 $41,635 $42,182 $41,803 $53,033 $60,568 $41,037 $50,388 $41,950 $44,660 $46,176 $41,420 $45,976 $47,956 $22,529 $48,842 $41,464 $40,285 $41,309 $43,160 $47,573 $44,057 $52,805 $53,046 $42,125 $46,214 $51,630 Table #9.3.4: Data of Income for Females $31,862 $40,550 $36,048 $30,752 $41,817 $40,236 $47,476 $40,500 $60,332 $33,823 $35,438 $37,242 $31,238 $39,150 $34,023 $33,745 $33,269 $32,684 $31,844 $34,599 $48,748 $46,185 $36,931 $40,416 $29,548 $33,865 $31,067 $33,424 $35,484 $41,021 $47,155 $32,316 $42,113 $33,459 $32,462 $35,746 $31,274 $36,027 $37,089 $22,117 $41,412 $31,330 $31,329 $33,184 $35,301 $32,843 $38,177 $40,969 $40,993 $29,688 $35,890 $34,381 Answer: Males Income N1: 52 df1 = N - 1 = 52 - 1 = 51 M1: $46,453.31 SS1: 1.08 s21 = 1.08/(52-1) = .45 Women’s Income N2: 52 df2 = N - 1 = 52 - 1 = 51