Question

RESEARCH SCENERIO A researcher conducts an independent-measures study examining the effectiveness of a group exercise program at an assisted living facility for elderly adults. One group of residents is selected to participate in the program, and a second group serves as a control. After 6 weeks, the researcher records a combined score measuring balance and strength for each individual. The data are as follows:

                                                Control               Exercise

                                                 n = 12                 n = 15

                                                M = 12                M = 15.5

                                               SS = 120.5        SS = 190.0

1. Show all four steps of hypothesis testing with an α = .05

2. write up your “statistical results” as they would appear in an APA journal

3. In the research scenario: Is there a chance of a Type I error?

4.   What is the independent variable?

5. What is the dependent variable?

Answer 1

Given that,
mean(x)=12
standard deviation , s.d1=3.309
number(n1)=12
y(mean)=15.5
standard deviation, s.d2 =3.683
number(n2)=15
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.201
since our test is two-tailed
reject Ho, if to < -2.201 OR if to > 2.201
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =12-15.5/sqrt((10.94948/12)+(13.56449/15))
to =-2.5967
| to | =2.5967
critical value
the value of |t α| with min (n1-1, n2-1) i.e 11 d.f is 2.201
we got |to| = 2.59669 & | t α | = 2.201
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -2.5967 ) = 0.025
hence value of p0.05 > 0.025,here we reject Ho
ANSWERS
---------------
1.
null, Ho: u1 = u2
alternate, H1: u1 != u2
2.
test statistic: -2.5967
critical value: -2.201 , 2.201
decision: reject Ho
p-value: 0.025
we have enough evidence to support the claim that difference of means effectiveness of a group exercise program at an assisted living facility for elderly adults.
3.
type 1 error is possible because it reject the null hypothesis
4.
the independent variable
An independent variable is the variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable.
5.
A dependent variable is the variable being tested and measured in a scientific experiment.