1:
yes it is paired data set.
2:
The difference should eb positive because we supposed that reading score increases for 4th graders.
3:
Following is the completed data:
3rd grade score | 4th grade score | d=4th grade score- 3rd garde score |
8.5 | 9.1 | 0.6 |
7.2 | 7.5 | 0.3 |
6.7 | 6.6 | -0.1 |
7.9 | 8.8 | 0.9 |
7.5 | 8.2 | 0.7 |
6.8 | 6.5 | -0.3 |
6.6 | 7.4 | 0.8 |
6.5 | 6.9 | 0.4 |
4.4 | 4.3 | -0.1 |
9.5 | 9.7 | 0.2 |
Total | 3.4 |
4:
The mean difference:
5:
Following table shows the calcualtions:
3rd grade score | 4th grade score | d=4th grade score- 3rd garde score | (d-mean)^2 |
8.5 | 9.1 | 0.6 | 0.0676 |
7.2 | 7.5 | 0.3 | 0.0016 |
6.7 | 6.6 | -0.1 | 0.1936 |
7.9 | 8.8 | 0.9 | 0.3136 |
7.5 | 8.2 | 0.7 | 0.1296 |
6.8 | 6.5 | -0.3 | 0.4096 |
6.6 | 7.4 | 0.8 | 0.2116 |
6.5 | 6.9 | 0.4 | 0.0036 |
4.4 | 4.3 | -0.1 | 0.1936 |
9.5 | 9.7 | 0.2 | 0.0196 |
Total | 3.4 | 1.544 |
6)
The degree of freedom: df=n-1=9
The critical value for 95% confidence interval is:2.262
The margin of error is
7:
The confidence interval is:
8:
Since confidence interval does not zero so the difference is significant.
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