Question

A researcher is interested in the possible effect(s) of exposure to environmental toxins on memory. She is able to collect tests of memory on pairs of twins, where one twin was exposed to the toxins and the other wasn’t. Higher scores indicate better memory performance. Do the data reflect an effect of the toxins on memory? Please use a t-test to demonstrate the result.

Twin A: 4 5 8 9 4

Twin B: 7 12 8 5 8

Answer 1

Ho :
Ha :

Level of Significance (l.o.s.) : = 0.05 (assumed)

Decision Criteria : Reject Ho at 5% l.o.s. if | t stat | > t crit,
t tab = t (/2, n1+n2-2) = t (0.025, 8) = 2.3060 (from t tables)
Calculations: In order to get the results, we make use of Excel and thus, following steps are needed to be followed:

Step 1 : Enter the data in Excel.
Step 2 : Select the "t-Test: Two-Sample Assuming Equal Variances" function from the data analysis package available under the data tab of MS-Excel.
Step 3 : Enter the range of Twin A in the first cell & that of Twin B in the second cell.
Step 4 : Click ok & thus, following results would be obtained :

t-Test: Two-Sample Assuming Equal Variances
	Twin A	Twin B
Mean	6	8
Variance	5.5	6.5
Observations	5	5
Pooled Variance	6
Hypothesized Mean Difference	0
df	8
t Stat	-1.290994449
P(T<=t) one-tail	0.116379869
t Critical one-tail	1.859548038
P(T<=t) two-tail	0.232759738
t Critical two-tail	2.306004135

Thus, t stat = -1.2910

Conclusion : Since | t stat | < t crit, we do not reject the Ho at 5% l.o.s. & thus conclude that there is no significant effect of the toxins on memory.

Hope this answers your query!