Question

4. People in a third state took the same literacy test mentioned in question 1. They retook the same literacy test after an educational intervention. Please test whether there is a difference between literacy-after and literacy-before.

   Literacy_after	Literacy_before
   10.1	6.8
   10.4	8
   9.6	7
   7.7	8.6
   10.3	7.5
   12	9.4
   12	6.2
   9.2	7.1
   10.5	5.9
   10.4	6.5
   10.5	7.5
   9.6	5.8
   8.8	8.9
   8.7	8.7
   9.7	6
   7	7

Answer 1

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses would be as follows :

Test statistic :

To test the hypothesis the most appropriate test is paired t-test. The test statistic is given as follows :

Where, is sample mean of the differences, s_{​​​​​​d} is sample standard deviation of the differences and n is sample size.

We have n = 16

From the above table we have,

The value of the test statistic is 5.2983.

P-value :

Since, our test is two-tailed test, therefore we shall obtain two-tailed p-value for the test statistic. The two-tailed p-value is given as follows :

P-value = 2.P(T > |t|)

We have, |t| = 5.2983

P-value = 2.P(T > 5.2983)

P-value = 0.0001

The p-value is 0.0001.

Decision :

In our question significance level is not given. Generally significance level of 0.05 or 0.01 is used. We shall significance level of 0.05.

Significance Level = 0.05

P-value = 0.0001

(0.0001 < 0.05)

Since, p-value is less than the significance level of 0.05, therefore we shall reject the null hypothesis (H_{​​​​​​0}) at 0.05 significance level.

Conclusion :

At 0.05 significance level, there is sufficient evidence to conclude that there is a difference between literacy-after and literacy-before.