Question

Performing a study on body-height, a researcher randomly measures the height of 25 persons in a football team A. The results turn out to be: {1.4, 1.9, 1.6, 1.9, 1.95, 1.73, 1.92, 1.75, 1.85, 1.79, 1.92, 1.77, 1.75, 1.64, 1.88, 1.68, 1.79, 1.85, 1.72, 1.44, 1.95, 1.82, 1.63, 1.6, 1.92}. In the literature, a result is found that 10 years before, the average height of persons in the football team A was determined to be 1.73.

Given that the acceptable threshold for significance is 5%, can this data be used to show that the average height of individuals in the football team A has increased in the last 10 years?

Answer 1

Given that,
population mean(u)=1.73
sample mean, x =1.766
standard deviation, s =0.1509
number (n)=25
null, Ho: μ=1.73
alternate, H1: μ>1.73
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.711
since our test is right-tailed
reject Ho, if to > 1.711
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1.766-1.73/(0.1509/sqrt(25))
to =1.193
| to | =1.193
critical value
the value of |t α| with n-1 = 24 d.f is 1.711
we got |to| =1.193 & | t α | =1.711
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value :right tail - Ha : ( p > 1.1928 ) = 0.1223
hence value of p0.05 < 0.1223,here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=1.73
alternate, H1: μ>1.73
test statistic: 1.193
critical value: 1.711
decision: do not reject Ho
p-value: 0.1223
we do not have enough evidence to support the claim that average height of individuals in the football team A has increased in the last 10 years