Question

21) The table below shows scores for 12 randomly selected students and their scores on the 1st and the 2nd SAT

Students	Scores on the 1st SAT	Scores on the 2nd Sat
1	392	532
2	421	523
3	439	427
4	340	607
5	493	444
6	457	490
7	396	428
8	400	524
9	510	532
10	409	397
11	413	550
12	339	357

a) At a 0.05, is there enough evidence to conclude that the students SAT scores improved on the second test?

b) Construct a 95% confidence interval for the mean difference.

Answer 1

Solution:

a) The null and alternative hypothesis is:

Under the null hypothesis, the test statistic is:

b) The 95% confidence interval is: