Question

The owner of a large apartment complex had an in-ground swimming pool installed in an effort to increase tenant satisfaction. Nine tenants were randomly selected to complete a questionaire that assessed their level of satisfaction with the apartment complex. Their scores before and after the installation of the pool are taken (before -after). The owner wants to assess the effectiveness of the pool in increasing tenant satisfaction.

a) state the hypothesis in symbols

b) indicate the type of t-test ( one sample two sample or paired?)

c) indicate if it is an observational study /survey or an experiment.

Answer 1

a.

Example problem
Assumed data,
null, H0: Ud = 0
alternate, H1: Ud > 0
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.86
since our test is right-tailed
reject Ho, if to > 1.86
we use Test Statistic
to= d/ (S/√n)
where
value of S^2 = [ ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 4.778
We have d = 4.778
pooled variance = calculate value of Sd= √S^2 = sqrt [ 559-(43^2/9 ] / 8 = 6.648
to = d/ (S/√n) = 2.156
critical Value
the value of |t α| with n-1 = 8 d.f is 1.86
we got |t o| = 2.156 & |t α| =1.86
make Decision
hence Value of | to | > | t α| and here we reject Ho
p-value :right tail - Ha : ( p > 2.1562 ) = 0.03158
hence value of p0.05 > 0.03158,here we reject Ho
ANSWERS
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b.
t test for paired data (before and after)
null, H0: Ud = 0
alternate, H1: Ud > 0
test statistic: 2.156
critical value: reject Ho, if to > 1.86
decision: Reject Ho
p-value: 0.03158
we have enough evidence to support the claim that The owner wants to assess the effectiveness of the pool in increasing tenant satisfaction.
c.
An observational study is a study where researchers simply collect data based on what is seen and heard and infer based on the data collected.
The researcher has no control over the variables in an observational study.
An experiment is a method of applying treatments to a group and recording the effects.