Question

1. An educational psychologist is interested in knowing whether the experience of attending preschool is related to subsequent sociability. She identifies two groups of first graders: those who had attended preschool and those who had not. Then each child is assigned a sociability score on the basis of observations made in the classroom and on the playground. Perform the 4 steps of hypothesis testing if using alpha is set at .05 for a two-tailed test.

The following sociability results are obtained:

Attended preschool Did not attend preschool

n1 = 12 n2 = 16

ΣX1 = 204 ΣX2 = 248

SS1 = 192 SS2 = 154

Answer 1

Suppose, random variables and denote sociability score of first graders who attended preschool and did not attend preschool respectively.

Here, two different groups of first graders are used to collect data. 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

Sample mean of first sample is given by

Sample mean of second sample is given by

Pooled sample variance is given by

Degrees of freedom

[Using R-code 'pt(-1.076742,26)+1-pt(1.076742,26)']

Level of significance

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 evidence that sociability score differs between first graders who attended preschool and who did not attend preschool.