Overview
Answer the following by underlining the correct answer (pls show work)
1.)
A. You perform a ?2 test and the calculated ?2 test value is 2.37 while the critical value marking off the extreme 5% of the distribution is 7.815. Based on these results, which of the following best describes the P value and conclusion for your ?2 test?
a) P<0.05 so you reject the null hypothesis
b) P>0.05 so you fail to reject the null hypothesis
c) P<0.05 so you fail to reject the null hypothesis
d) P>0.05 so you reject the null hypothesis
B. You perform a ?2 test and the calculated ?2 test value is 17.2 while the critical value marking off the extreme 5% of the distribution is 7.815. Based on these results, which of the following best describes the P value and conclusion for your ?2 test?
a) P<0.05 so you reject the null hypothesis
b) P>0.05 so you fail to reject the null hypothesis
c) P<0.05 so you fail to reject the null hypothesis
d) P>0.05 so you reject the null hypothesis
C. You perform a ?2 test with 4 df and the calculated ?2 test value is 6.3. Based on these results and using an ? level of 0.05, which of the following best describes the P value and conclusion for your ?2 test? (Hint: you must look up the critical value on the ?2 table)
a) P<0.05 so you reject the null hypothesis
b) P>0.05 so you fail to reject the null hypothesis
c) P<0.05 so you fail to reject the null hypothesis
d) P>0.05 so you reject the null hypothesis
D. You perform a ?2 test with 1 df and the calculated ?2 test value is 3.9. Based on these results and using an ? level of 0.05, which of the following best describes the P value and conclusion for your ?2 test?
a) P<0.05 so you reject the null hypothesis
b) P>0.05 so you fail to reject the null hypothesis
c) P<0.05 so you fail to reject the null hypothesis
d) P>0.05 so you reject the null hypothesis
E. You perform a ?2 test of independence (contingency test) to examine the association between two categorical variables. The raw data table is a 3x4 table (three columns and four rows of data). The calculated ?2 test value is 11.5. Based on this results and using an ? level of 0.05, which of the following best describes the P value and conclusion for your ?2 test?
a) P<0.05 so you reject the null hypothesis
b) P>0.05 so you fail to reject the null hypothesis
c) P<0.05 so you fail to reject the null hypothesis
d) P>0.05 so you reject the null hypothesis
2.) A study in Sweden examined the occurrence of arthritis in elite soccer players. They measured the frequency of arthritis in the knees and hips of elite soccer players in their mid 50’s, people of the same age who had played soccer but not at the elite level, and people of the same age that had not played soccer. Conduct a X2 analysis to examine whether there is a relationship between playing soccer and the occurrence of arthritis.
Elite
Non-elite
Did not play
Total
Arthritis
10
9
24
43
No arthritis
61
206
548
815
Total
71
215
572
858
A. Fill in the table:
O
E
O-E
(O-E)2
(O-E)2/E
10
9
24
61
206
548
?2=
B. Null hypothesis:
C. Alternate hypothesis:
D. Type of ?2 test: _______________
E. ?2 Value: ___________ F. Critical ?2 (? = 0.05): ________________
G. DF: ________________ H. P = ______________________
I. Conclusion (Write your conclusion in plain English followed by TECHNICAL language):
3.)Investigators developed a vaccine that they hope will prevent cholera. Some individuals in a small Haitian village agree to be vaccinated with an experimental version because cholera is spreading through Haiti. After cholera hits the village, scientists collect data on the occurrence of cholera in members of the village that were vaccinated and those that were not. Test whether there is evidence that the vaccine provided protection against cholera (being vaccinated and not coming down with cholera are related).
Infected with cholera
Not infected with cholera
Total
Vaccinated
11
89
100
Unvaccinated
21
79
100
Total
32
168
200
A. Fill in the table:
O
E
O-E
(O-E)2
(O-E)2/E
11
89
21
79
?2=
B. Null hypothesis:
C. Alternate hypothesis:
D. Type of ?2 test: _________________________
E. ?2 Value: __________ F. Critical ?2 (? = 0.05): _______________
G. DF: ________________ H. P : ______________________
I. Conclusion (Write your conclusion in plain English followed by TECHNICAL language):
4.) A population of birds is polymorphic for color, with some individuals being dark brown, some beige, and some bright yellow. The variation in color is known to be due to a single genetic locus, with two alleles, “A” and “a”. Birds with genotype “AA” are brown, birds with genotype “Aa” are beige, and birds with genotype “aa” are yellow. Historically, allele “A” had a frequency (p) of 0.7 and allele “a” had a frequency (q) of 0.3. Remember that assuming Hardy-Weinberg equilibrium, the expected frequencies for brown (AA), beige (Aa), and yellow (aa) birds would be p2, 2pq, and q2 respectively.
An ornithologist samples the population and finds 92, brown birds, 85 beige birds, and 23 yellow birds among the 200 birds observed. Do these proportions fit the expected distribution for the color morphs assuming that the allele frequencies for “A” and “a” are 0.7 and 0.3 respectively and the population is in Hardy Weinberg equilibrium? Note that because the expected genotype frequencies are calculated from the alelle frquencies, you lose another DF in the problem. The DF would be 3 (number of classes) – 1 (the typical 1 df you lose with a ?2 test of goodness of fit) – 1 (because allele frequencies are used to calculate expected genotype frequencies) = 1 (so 3-1-1= 1 df).
A. Fill in the table:
O
E
O-E
(O-E)2
(O-E)2/E
Brown
92
Beige
85
Yellow
23
Total=
200
?2=
B. Null hypothesis:
C. Alternate hypothesis:
D. Type of ?2 test: _________________________
E. ?2 Value: ________________ F. Critical ?2 (? = 0.05): ___________________
G. DF: ______1 (given)____________ H. P : _________________________
I. Conclusion (Write your conclusion in plain English followed by TECHNICAL language):
5.)Pygmy grasshoppers come in two colors, a normal color morph that is brown and a melanistic morph that is black. The melanistic form tends to be more common in areas that have been recently ravaged by fire, presumably because they blend in better with the background there and are thus less susceptible to bird predation. Entomologists are interested in knowing whether color morph is associated with dispersal potential. Some pygmy grasshoppers are winged and are prone to disperse while others lack functional wings and are thus not likely to disperse. Data are collected on the number of normal brown and melanistic grasshoppers that have functional wings and that lack functional wings. The counts of each type are listed below.
Test whether color morph and dispersal ability (as evidenced by wings) are significantly associated in these pygmy grasshoppers.
Melanistic
Normal Color
Total =
Winged
20
27
47
Wingless
13
25
38
Total=
33
52
85
A. Fill in the table:
O
E
O-E
(O-E)2
(O-E)2/E
20
27
13
25
?2=
B. Null hypothesis:
C. Alternate hypothesis:
D. Type of ?2 Test: _____________________________
E. Test statistic: _______________ F. Critical value (? = 0.05): _____________
G. DF: ___________________ H. P : _________________________
i. Conclusion (in plain English followed by technical description):