Infection of chickens with the avian flu is a threat to both poultry production
ID: 2934150 • Letter: I
Question
Infection of chickens with the avian flu is a threat to both poultry production and human health. A research team created transgenic chickens resistant to avian flu infection. Could the modification affect chickens in other ways? The researchers compared the hatching weights (in grams) of 44 transgenic chickens and 54 independently selected commercial chickens of the same breed. The data are displayed below. Does the data show significant evidence (with alpha of 0.05) that the population of transgenic chickens differs in mean hatching weight from the population of commercial chickens of the same breed?
A. Perform a T-test to address the research question. For the non-practical skill questions, you can use the unpooled method as default.
B. a) perform an appropriate test for the hypothesis test and verify the condition of the method.
Check list:1) are the two samples independent or dependent?
2) Can CLT be applied to both samples?
3) Check whether, and then decide whether to use pooled or unpooled method. Report just one and justify your choice.
Trangenic
Commercial
43.96298976
41.25625387
43.55780639
46.74801359
44.06087649
42.67744392
43.38919304
47.41403423
40.37162237
43.68586519
46.99128382
32.53857544
42.45022886
40.91789625
48.88614232
46.98047472
48.8187156
32.37787035
40.28768722
38.82700752
45.09371304
46.17889381
32.58797397
53.9431311
48.34630667
46.11337676
40.31268852
44.2315875
46.93955085
47.42896614
42.57821806
41.94907068
37.90231673
45.27244291
47.15923159
49.09138641
37.84130192
39.29374829
43.02569245
44.21535806
45.59146328
35.0070096
48.70042908
44.54871548
47.08370481
43.67135003
47.36084345
43.43569334
39.51285023
46.35431309
41.67805461
41.68701704
42.24327658
44.88855581
42.06520231
45.69410487
41.31345737
41.79419856
33.97814218
46.26775917
42.68090518
42.83483924
41.29866043
47.71362672
39.98579689
45.29158447
48.13502315
47.34873075
43.26519077
44.40664317
47.69089636
45.50663755
44.45467474
42.55957591
41.95861612
45.5559117
39.26397579
50.36851981
49.65531383
42.38114577
39.1199184
46.21670986
43.28813574
45.60699726
41.61344083
44.13353719
45.13172864
43.35595521
48.62790562
44.79204163
41.86203835
43.46589267
45.70639386
40.19515533
40.67207556
50.67428496
41.89866445
42.74772255
Trangenic
Commercial
43.96298976
41.25625387
43.55780639
46.74801359
44.06087649
42.67744392
43.38919304
47.41403423
40.37162237
43.68586519
46.99128382
32.53857544
42.45022886
40.91789625
48.88614232
46.98047472
48.8187156
32.37787035
40.28768722
38.82700752
45.09371304
46.17889381
32.58797397
53.9431311
48.34630667
46.11337676
40.31268852
44.2315875
46.93955085
47.42896614
42.57821806
41.94907068
37.90231673
45.27244291
47.15923159
49.09138641
37.84130192
39.29374829
43.02569245
44.21535806
45.59146328
35.0070096
48.70042908
44.54871548
47.08370481
43.67135003
47.36084345
43.43569334
39.51285023
46.35431309
41.67805461
41.68701704
42.24327658
44.88855581
42.06520231
45.69410487
41.31345737
41.79419856
33.97814218
46.26775917
42.68090518
42.83483924
41.29866043
47.71362672
39.98579689
45.29158447
48.13502315
47.34873075
43.26519077
44.40664317
47.69089636
45.50663755
44.45467474
42.55957591
41.95861612
45.5559117
39.26397579
50.36851981
49.65531383
42.38114577
39.1199184
46.21670986
43.28813574
45.60699726
41.61344083
44.13353719
45.13172864
43.35595521
48.62790562
44.79204163
41.86203835
43.46589267
45.70639386
40.19515533
40.67207556
50.67428496
41.89866445
42.74772255
Explanation / Answer
A. Perform a T-test to address the research question. For the non-practical skill questions, you can use the unpooled method as default.
Solution:
We have to use T test for checking whether there is any significant difference observed in the two population means. The null and alternative hypotheses are given as below:
Null hypothesis: H0: There is no any statistically significant difference in the Average weight of transgenic chicken and average weight of commercial chicken.
Alternative hypothesis: Ha: There is a statistically significant difference in the average weight of the transgenic chicken and average weight of commercial chicken.
H0: µtrangenic = µcommercial
Ha: µtrangenic µcommercial
This is a two tailed test.
We are given level of significance = = 0.05
The test statistic formula is given as below:
t = (X1bar – X2bar) / sqrt[(S1^2/N1)+(S2^2/N2)]
From the given data for samples, we have
X1bar = 44.68269224
X2bar = 42.85199047
S1 = 3.1548, S1^2 = 9.952815197
S2 = 4.2803, S2^2 = 18.32078544
N1 = 44
N2 = 54
DF = N1 + N2 – 2 = 44 + 54 -2 = 96
S1^2/N1 = 9.952815197/44 = 0.226200345
S2^2/N2 = 18.32078544/54 = 0.339273804
[(S1^2/N1)+(S2^2/N2)] = 0.226200345 + 0.339273804 = 0.565474149
sqrt[(S1^2/N1)+(S2^2/N2)] = sqrt(0.565474149) = 0.751980152
(X1bar – X2bar) = 44.68269224 - 42.85199047 = 1.83070177
t = (X1bar – X2bar) / sqrt[(S1^2/N1)+(S2^2/N2)]
t = 1.83070177/ 0.751980152
t = 2.434508099
Lower critical value = -1.9850
Upper critical value = 1.9850
P-value = 0.0168
(Critical value and P-value are calculated by using t-table or excel)
P-value < = 0.05
So, we reject the null hypothesis that there is no any statistically significant difference in the Average weight of transgenic chicken and average weight of commercial chicken.
There is sufficient evidence to conclude that there is a statistically significant difference in the Average weight of transgenic chicken and average weight of commercial chicken.
Question B.a.
For the above two sample t test, given two samples are independent from each other and observations are independent. There is no any relationship exists between the two samples and sample sizes for both samples are unequal.