Question

Most bats are very poor at walking, but the vampire bar is an exception. It is not clear why bats are poor walkers from a mechanical perspective, although a leading hypothesis has been that their hind legs are too weak. A test of this hypothesis was performed, measuring the strength of the hind legs of an insectivorous bat that walks poorly to the hind-leg strength of a vampire bat. Six individuals of the insectivore bat were measured, with an average hind-leg strength of 93.5 and a std. dev. of 36.6. The mean hind-leg strength for six vampire vats was 68.3, with a std. dev. of 8.1. Using this information, answer the following two questions: 1. Assuming that these measures of strength were normally distributed within groups, what is the appropriate test of comparing the mean hind-leg strength of these two species? 2. Look at the results closely. Without performing a statistical test, comment on the hypothesis that insufficient hind-leg strength is the reason that the insectivorous bat species cannot walk as well as the vampire bat species.

Answer 1

Given that,
mean(x)=93.5
standard deviation , s.d1=36.6
number(n1)=6
y(mean)=68.3
standard deviation, s.d2 =8.1
number(n2)=6
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.571
since our test is two-tailed
reject Ho, if to < -2.571 OR if to > 2.571
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =93.5-68.3/sqrt((1339.56/6)+(65.61/6))
to =1.6467
| to | =1.6467
critical value
the value of |t α| with min (n1-1, n2-1) i.e 5 d.f is 2.571
we got |to| = 1.64669 & | t α | = 2.571
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.6467 ) = 0.161
hence value of p0.05 < 0.161,here we do not reject Ho
ANSWERS
---------------
1.
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.6467
critical value: -2.571 , 2.571
decision: do not reject Ho
p-value: 0.161
we do not have enough evidence to support the claim that comparing the mean hind-leg strength of these two species
2.
Without performing a statistical test, the hypothesis that
insufficient hind-leg strength is the reason that the insectivorous bat species cannot walk
as well as the vampire bat species because it fails to reject the null hypothesis.