Question

AM -vs- PM Height: We want to test the claim that people are taller in the morning than in the evening. Morning height and evening height were measured for 33 randomly selected adults and the difference (morning height) − (evening height) for each adult was recorded. The mean difference was 0.21 cm with a standard deviation of 0.39 cm. Use this information to test the claim that on average people are taller in the morning than in the evening. Test this claim at the 0.05 significance level.

(b) What is the test statistic? Round your answer to 2 decimal places.

t

x

=   

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.

P-value =

Answer 1

Assume data, because not given in the data
population mean(u)=23
sample mean, x =23.21
given data,
standard deviation, s =0.39
number (n)=33
null, Ho: μ=23
alternate, H1: μ>23
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.694
since our test is right-tailed
reject Ho, if to > 1.694
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =23.21-23/(0.39/sqrt(33))
to =3.0932
| to | =3.0932
critical value
the value of |t α| with n-1 = 32 d.f is 1.694
we got |to| =3.0932 & | t α | =1.694
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :right tail - Ha : ( p > 3.0932 ) = 0.00204
hence value of p0.05 > 0.00204,here we reject Ho
ANSWERS
---------------
null, Ho: μ=23
alternate, H1: μ>23
b.
test statistic: 3.0932
critical value: 1.694
decision: reject Ho
c.
p-value: 0.00204
we have enough evidence to support the claim that on average people are taller in the morning than in the evening.