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AP Biology Chi-‐square Practice Problems, Study notes of Biology

University of Luxemburg (UL)Biology

AP Biology Chi-‐square Practice Problems. 1. The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in ...

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2021/2022

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AP#Biology#Chi,square#Practice#Problems#
1. The#age#distribution#of#the#Canadian#population#and#the#age#distribution#of#a#random#sample#of#455#residents#in#the#Red#
Lake#Village#of#the#Northwest#Territories#are#shown#below.##Use#the#chi#square#test#to#determine#if#the#age#distribution#in#
Red#Lake#is#significantly#different#(p#=#0.05)#from#the#general#Canadian#population.#
Age#(years)#
%#of#Canadian#population#
Observed#number#in#Red#Lake#
Under#5#
7.2%#
47#
5#to#14#
13.6%#
75#
15#to#64#
67.1%#
288#
65#and#older#
12.1%#
45#
#
Outcomes#
O#
E#
O#–#E#
(O#–#E)2/E#
Under&5&
47&
33&
14&
5.94&
5&to&14&
75&
62&
13&
2.73&
15&to&64&
288&
305&
417&
0.95&
65&and&older&
45&
55&
410&
1.82&
total&
455&
455&
&
Σ#=#11.44#
#
Conclusion:##D&of&F&=&4&–&1&=&3&;&CV&for&3&D&of&F&=&7.82&;&11.84&>&7.82&;&REJECT&null&hypothesis&;&age&dist.&changed&significantly#
#
#
2. Using#binoculars,#volunteers#observed#feeding#habits#of#a#random#sample#of#320#deer,#as#shown#below.##Use#chi#square#to#
test#the#hypothesis#that#the#natural#distribution#of#plants#fits#the#deer#feeding#pattern.#
Observed#Feeding#Area#
Plant#Composition#in#Area#
Observed###of#Deer#Feeding#in#Area#
Area#A#
32%#
102#
Area#B#
38.7%#
125#
Area#C#
12%#
43#
Area#D#
9.3%#
27#
Area#E#
8%#
23#
#
Outcomes#
O#
E#
O#–#E#
(O#–#E)2#
(O#–#E)2/E#
Area&A&
102&
102&
0&
0&
0&
Area&B&
125&
124&
1&
1&
0.01&
Area&C&
43&
38&
5&
25&
0.66&
Area&D&
27&
30&
43&
9&
0.3&
Area&E&
23&
26&
43&
9&
0.35&
total&
320&
320&
&
&
Σ#=##1.32#
#
Conclusion:#D&of&F&=&5&–&1&=&4&;&CV&for&4&D&of&F&=&9.49&;&1.32&<&9.49&;&ACCEPT&null&hypothesis&;&plant&distr.&fits&deer&distr.#
#
#
3. The#Fish#and#Game#Department#stocked#Lake#Lulu#with#fish#in#the#following#proportions:#30%#catfish,#15%#bass,#40%#
bluegill,#and#15%#pike.##Five#years#later,#they#sampled#500#fish#in#the#lake#to#see#if#the#distribution#of#fish#had#changed,#as#
shown#below.##Use#the#chi#square#test#to#determine#if#the#distribution#of#fish#changed#significantly#(p#=#0.05)#in#the#5,year#
interval.#
Catfish#=#120,#Bass#=#85,#Bluegill#=#220,#Pike#=#75#
Outcomes#
O#
O#–#E#
(O#–#E)2/E#
Catfish&
120&
430&
6&
Bass&
85&
10&
1.33&
Bluegill&
220&
20&
2&
Pike&
75&
0&
0&
total&
500&
&
Σ#=##9.33#
#
Conclusion:#D&of&F&=&4&–&1&=&3&;&CV&for&3&D&of&F&=&7.82&;&9.33&>&7.82&;&REJECT&null&hypothesis&;&fish&distr.&changed&signif.&In&5&yrs.#

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AP Biology Chi-­‐square Practice Problems

  1. The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Red Lake Village of the Northwest Territories are shown below. Use the chi square test to determine if the age distribution in Red Lake is significantly different (p = 0.05) from the general Canadian population. Age (years) % of Canadian population Observed number in Red Lake Under 5 7.2% 47 5 to 14 13.6% 75 15 to 64 67.1% 288 65 and older 12.1% 45 Outcomes O E O – E (O – E) 2 (O – E) 2 /E Under 5 47 33 14 196 5. 5 to 14 75 62 13 169 2. 15 to 64 288 305 -­‐ 17 289 0. 65 and older 45 55 -­‐ 10 100 1. total 455 455 Σ = 11. Conclusion: D of F = 4 – 1 = 3 ; CV for 3 D of F = 7.82 ; 11.84 > 7.82 ; REJECT null hypothesis ; age dist. changed significantly
  2. Using binoculars, volunteers observed feeding habits of a random sample of 320 deer, as shown below. Use chi square to test the hypothesis that the natural distribution of plants fits the deer feeding pattern. Observed Feeding Area Plant Composition in Area Observed # of Deer Feeding in Area Area A 32% 102 Area B 38.7% 125 Area C 12% 43 Area D 9.3% 27 Area E 8% 23 Outcomes O E O – E (O – E)^2 (O – E)^2 /E Area A 102 102 0 0 0 Area B 125 124 1 1 0. Area C 43 38 5 25 0. Area D 27 30 -­‐ 3 9 0. Area E 23 26 -­‐ 3 9 0. total 320 320 Σ = 1. Conclusion: D of F = 5 – 1 = 4 ; CV for 4 D of F = 9.49 ; 1.32 < 9.49 ; ACCEPT null hypothesis ; plant distr. fits deer distr.
  3. The Fish and Game Department stocked Lake Lulu with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later, they sampled 500 fish in the lake to see if the distribution of fish had changed, as shown below. Use the chi square test to determine if the distribution of fish changed significantly (p = 0.05) in the 5-­‐year interval. Catfish = 120, Bass = 85, Bluegill = 220, Pike = 75 Outcomes O E O – E (O – E)^2 (O – E)^2 /E Catfish 120 150 -­‐ 30 900 6 Bass 85 75 10 100 1. Bluegill 220 200 20 400 2 Pike 75 75 0 0 0 total 500 500 Σ = 9. Conclusion: D of F = 4 – 1 = 3 ; CV for 3 D of F = 7.82 ; 9.33 > 7.82 ; REJECT null hypothesis ; fish distr. changed signif. In 5 yrs.