Question

The article "Genetic Tweak Turns Promiscuous Animals into Loyal Mates" (Los Angeles Times, June 17, 2004) summarizes a research study that appeared in the June 2004 issue of Nature. In this study, 11 male meadow voles that had a single gene introduced into a specific part of the brain were compared to 20 male meadow voles that did not undergo this genetic manipulation. All of the voles were paired with a receptive female partner for 24 hours. At the end of the 24-hour period, the male was placed in a situation where he could choose either the partner from the previous 24 hours or a different female. The percentage of the time that the male spent with his previous partner during a 24-hour time period was recorded. The accompanying data (see link below) are approximate values read from a graph in the Nature article. Assume that the population is normally distributed and that these voles are representative of their respective populations (population #1 is genetically altered male voles and population #2 is non genetically altered voles).
Do these data support the researchers hypothesis that the mean percentage of the time spent with the previous partner is significantly greater for the population of genetically altered voles than for the population of voles that did not have the gene introduced? Test the relevant hypotheses using α=.05.

genetically_altered,not_genetically_altered
59,2
62,5
73,13
80,28
84,34
85,40
89,48
92,50
92,51
93,54
100,60
,67
,70
,76
,81
,84
,85
,92
,97
,99
(Note on rounding: if you round at intermediate steps while calculating your test statistic, please go out to at least 3 decimal places).

What is the an appropriate pair of hypotheses?

H₀: μ₁ - μ₂ > 0 H_a: μ₁ - μ₂ = 0

H₀: μ₁ - μ₂ = 0 H_a: μ₁ - μ₂ < 0     

H₀: μ₁ - μ₂ = 0 H_a: μ₁ - μ₂ > 0.

H₀: μ₁ - μ₂ < 0 H_a: μ₁ - μ₂ = 0

What is the value of the test statistic? Round this answer to 1 decimal place.
t =  

Calculate the P-value. Round this answer to 3 decimal places.
P-value =  

What conclusion can you draw?

Fail to reject the null hypothesis. We have evidence that the mean percentage of the time spent with the previous partner is significantly greater for the population of genetically altered voles than for the population of voles that did not have the gene introduced.

Reject the null hypothesis. We do not have evidence that the mean percentage of the time spent with the previous partner is significantly greater for the population of genetically altered voles than for the population of voles that did not have the gene introduced.     

Fail to reject the null hypothesis. We do not have evidence that the mean percentage of the time spent with the previous partner is significantly greater for the population of genetically altered voles than for the population of voles that did not have the gene introduced.

Reject the null hypothesis. We have evidence that the mean percentage of the time spent with the previous partner is significantly greater for the population of genetically altered voles than for the population of voles that did not have the gene introduced.

Answer 1

Given that,
mean(x)=82.5455
standard deviation , s.d1=13.0258
number(n1)=11
y(mean)=56.8
standard deviation, s.d2 =29.7491
number(n2)=20
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.812
since our test is right-tailed
reject Ho, if to > 1.812
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =82.5455-56.8/sqrt((169.67147/11)+(885.00895/20))
to =3.333
| to | =3.333
critical value
the value of |t α| with min (n1-1, n2-1) i.e 10 d.f is 1.812
we got |to| = 3.33276 & | t α | = 1.812
make decision
hence value of | to | > | t α| and here we reject Ho
p-value:right tail - Ha : ( p > 3.3328 ) = 0.00379
hence value of p0.05 > 0.00379,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 3.333
critical value: 1.812
decision: reject Ho
p-value: 0.00379
we have enough evidence to support the claim that the mean percentage of the time spent with the previous partner is significantly greater for the population of genetically
altered voles than for the population of voles that did not have the gene introduced