Question

As part of an educational experiment a sample of sixteen Year 3 children was randomly divided into two groups, each of size eight.
The first group of eight children was taught arithmetic by the use of traditional procedures, whilst the second group of eight was taught arithmetic by newer modern methods.
At the end of the year all 16 children sat for an arithmetic achievement test, and also an arithmetic understanding test.
The marks(out of 100) obtained by the children are shown in the following tables.

Group 1 (Traditional)			Group 2 (Modern)
Child	Achievement Marks	Understanding Marks	Child	Achievement Marks	Understanding Marks
A	71	67	I	67	51
B	53	60	J	68	66
C	62	69	K	60	62
D	62	60	L	54	64
E	66	63	M	68	68
F	71	56	N	52	64
G	66	65	O	52	74
H	61	54	P	59	60

In answering the following questions you may assume that both achievement marks and understanding marks are normally distributed.

1. To test whether there is a significant difference between the mean Achievement mark and the mean Understanding mark of children taught by the Modern method we would carry out ( A. A paired t test B. A two sample t test)

2. To test whether there is a significant difference between the mean Achievement marks of children taught by the Traditional method and of children taught by the Modern method.  (A. A paired t test B. A two sample t test)

3. To test whether there is a significant difference between the mean Achievement mark and the mean Understanding mark of children taught by the Traditional method we would carry out . (A. A paired t test B. A two sample t test)

4. To test whether there is a significant difference between the mean Understanding marks of children taught by the Traditional method and of children taught by the Modern method. (A. A paired t test B. A two sample t test)

Answer 1