3.Five university students were given an English achievement test before and after receiving instruction in basic grammar. Their scores are shown below:

Student

Before

After

A

20

18

B

18

22

C

17

15

D

16

17

E

12

9

Should we conclude that future students would show higher scores after instruction? Use the .05 significance level. Use hypothesis testing.

Step 1:

Population 1: Students before receiving instruction

Population 2: Students after receiving instruction

Null Hypothesis: H₀ There will be no change of score between Population 1 and 2.

Research Hypothesis: H₁ Population 2 scores will be higher than Population 1.

Population 1 M = (20+18+17+16+12)/5 = 83/5 = 16.6

Population 2 M = (18+22+15+17+9)/5 = 81/5 = 16.2

Step 2:

S² = (X - M)² / N -1 =

S² = 76/5-1 = 19

S² = (18-16.2)2 + (22-16.2)2 + (15-16.2)2 + (17-16.2)2 + (9-16.2)2/ 5-1

90.8/4 = 22.7

Estimated population variance: 22.7

The variance of the distribution of means: 22.7/5 = 4.54

The standard deviation of the distribution of means: 4.54 = 2.13

Degrees of freedom: N-1 = 5-1= 4

Step 3:

The level of significance is 0.5 with a one tailed test, the cutoff is 2.132

Step 4:

t = M - Population M / S_M

t = (16.2 - 16.4)/2.13

My question is... why is the population mean stated as 16.4 and not 16.6 like in the initial population 1 for step 1?