Question

The world's smallest mammal is the bumblebee bat, also known as the kitti's hog-nosed bat. Such bats are roughly the size of a large bumblebee. Listed below are weights (in grams) from a sample of these bats:

1.7, 1.6, 1.5, 2.0, 2.3, 1.6, 1.6, 1.8, 1.5, 1.7,

2.3, 1.3, 1.5, 1.6, 2.0

(a) Use the sample data to construct a 95% confidence interval of the mean weight and state the margin of error (E).

(b) Using a 0.05 significance level to test the claim that these bats come from the same population having a mean weight equal to 1.8 g. What is your conclusion of the claim after the test? (Need to state hypotheses, compute test statistic, critical value, P-value, and conclusion)

Answer 1

Sol:

For the given sample mean and standard deviations are found using R

bats <- c(1.7, 1.6, 1.5, 2.0, 2.3, 1.6, 1.6, 1.8, 1.5, 1.7,
2.3, 1.3, 1.5, 1.6, 2.0)
> mean(bats)
[1] 1.733333
> sd(bats)
[1] 0.294392
> length(bats)
[1] 15

mean=xbar=1.733333

standard deviation=s=0.294392

sample size=n=15

alpha=0.05

alpha/2=0.05/2=0.025

df=n-1=15-1=14

t critical ==T.INV(0.025,14)=2.144786688

margin of error=E=t*s/sqrt(n)

=2.144786688*0.294392/sqrt(15)

=0.1630289

95% confidence interval

sample mean -margin of error,sample mean+margin of error

1.733333-0.1630289,1.733333+0.1630289

1.570304, 1.896362

Solution-b:

Ho:Mu=1.8

Ha:Mu not=1.8

alpha=0.05

test statistic

t=xbar-mu/s/sqrt(n)

=(1.733333-1.8)/(0.294392/sqrt(15))

t=-0.8770625

df=n-1=15-1=14

p value in excel=

=T.DIST.2T(0.8770625,14)

=0.395254098

p>0.05

Fail to reject Ho

Accept Ho

There is suffcient statistical evidence at 5% level of significance to conclude that these bats come from the same population having a mean weight equal to 1.8 g