Question

A student is curious whether taking a test in the same room as the lecture will influence test performance. To test this she selects 30 students at random and assigns them randomly to two groups. Group 1 takes their test in a new classroom environment. Group 2 takes their test in the same room as the class lectures. The student thinks that taking the test in the same room as the lecture will improve performance. At a conservative 1% significance level (in other words, two-tailed), do the data suggest that room placement influences performance? Calculate the corresponding confidence interval and an effect size. Group 1: Mean = 20, SD = 3, N = 11 Group 2: Mean = 16, SD = 3, N = 19

Answer 1

Problem:
Hypothesis to determine if the room placement influences performance of the students

Null Hypothesis:
Ho:The mean difference of marks of the 2 group of students is same
Alternate Hypothesis:
H1:The mean difference of marks of the 2 group of students is not same
We will test the hypothesis at 1% level of significance.

If |calculated test statistic|> t(/2,n1+n2-2) we reject the null hypothesis.

tabulated value of t using( n1+n2-2=11+19-2=28) 28 df and =0.01:
The critical value is: 2.763

The test statistics is given as:

Where Sp is the the pooled standard deviation which is given as:

x1=20
x2=16
Sp=3
t*=(20-16)/(3*(1/11+1/19)^0.5)

t*=3.519

ince |calculated t|(3.519)> tabulated t(2.763) we reject Ho at 1% level of significance and conclude that the mean difference of marks of the 2 group of students is not same.i.e to say the room placement effects the performance of the students.

The confidence Interval is given as

The confidence Interval is:(0.86,7.14)

The effect size is given as:

We have calculated hedges' g because of unequal sizes.

hedges' g= 1.2972973

converted r=0.5432771