In: Statistics and Probability
. Independent samples t-test:
You want to test whether plants grow better when you talk to them. You obtain two sets of philodendrons, talk to one set and ignore the other (except to water them). After 6 months, you measure their growth in inches. The data are below. Conduct an independent samples t-test with alpha = .05 with a nondirectional test to determine if there was a significant difference between the two sets of plants.
Answer the following questions. You can use SPSS for this problem, but if you do this “by hand” be sure to show your work.
Not talked to Talked to
4 8
2 7
8 13
4 6
6 5
6 11
3 8
5 9
6 10
a)
Ho : µ1 = µ2
Ha : µ1 ╪ µ2
b) Degree of freedom, DF= n1+n2-2 = 16
c) critical t value = ± 2.120 (excel formula =t.inv(α/2,df)
d)
Sample #1 ----> 1
mean of sample 1, x̅1= 4.89
standard deviation of sample 1, s1 =
1.83
size of sample 1, n1= 9
Sample #2 ----> 2
mean of sample 2, x̅2= 8.56
standard deviation of sample 2, s2 =
2.51
size of sample 2, n2= 9
difference in sample means = x̅1-x̅2 =
4.8889 - 8.6 =
-3.67
pooled std dev , Sp= √([(n1 - 1)s1² + (n2 -
1)s2²]/(n1+n2-2)) = 2.1953
std error , SE = Sp*√(1/n1+1/n2) =
1.0349
t-statistic = ((x̅1-x̅2)-µd)/SE = (
-3.6667 - 0 ) /
1.03 = -3.5431
e) Decision: | t-stat | > | critical value |, so,
Reject Ho
f)
effect size,
cohen's d = |( x̅1-x̅2 )/Sp | =
1.6702
g) t(16) = -3.54 , reject the null hypothesis
h) There is enough evidence of significant difference