Answer to Question #110400 in Statistics and Probability for Mateus Michael Ndinomwene

Question

In a study of the mating calls of the tree toad Hyla, Littlejohn (1965) found the duration
of the call in a sample of 29 observations to have a mean of 189 ms (milliseconds) and a
standard deviation of 31.0 ms.
(a) Construct the 95 % confidence interval to the mean call duration (5)
(b) Construct the 90 % confidence interval to the mean call duration (5)
(c) Interpret what these confidence intervals signify and explain why they are different

Answer 1

a) 95% confidence interval

CI =mean ± margin error (E)

E=$Z_c\frac {\sigma} {\sqrt n}$

=$1.96*\frac {31}{\sqrt {29}}$

=11.2828

CI=189±11.2828

=(177.7172,200.2828)

b) 90% confidence interval

=$1.64*\frac {31}{\sqrt {29}}$

=9.4408

CI= 189±9.4408

=(179.5592, 198.4408)

c) These confidence intervals signify the range in which the population parameter lies. The values are different because the confidence levels are different. A higher confidence level has a wider confidence width.