Question

2.   A researcher wants to determine whether children will learn concepts better with
positive examples alone or with both positive and negative ones. Twenty children are recruited to participate and ten are randomly assigned to each of the two experimental conditions. Their scores on the concept-formation task are given below (higher scores indicate better performance). Decide whether there is a difference between the two methods. Be sure to complete all 8 steps of the Hypothesis Testing procedure. Use an alpha level of .05.

       Positive Only       Positive & Negative

           8                       14
           10                       8
           7                       7
           12                       10
           6                       12
           9                       6
           10                       15
           11                       11
           6                       9
           13                       8

Answer 1

2.

Here, two different groups consisting 10 children each are used to collect data in two different situations. Further we do not know population standard deviation (or variance). So, we have to perform two sample t-test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

First sample size

Second sample size

Degrees of freedom

Level of significance

[Using R-code '1-pt(0.6566108,18)+pt(-0.6566108,18)']

We reject our null hypothesis if

Here, we observe that

So, we cannot reject our null hypothesis.

Hence, based on the given data we can conclude that there is no significant difference between children's learning concepts with positive examples alone or with both positive and negative ones.