Question

1. We have two samples of people who took a literacy test, termed Literacy A and Literacy B which are from two different states. Researches are interested if there's a difference in literacy between the two states. First use folded F test to see if the varianceare equal or not, then T- test

   

Literacy A	Literacy B
9.6	24
8.9	10
11.4	20.7
7.2	11.4
9.2	4
-0.3	-4.5
2.2	22.2
-4.5	-4.5
6.6	6.6
7.3	7.3
11.5	11.5
8.6	8.6
3.4	3.4
2.2	2.2
18.4	18.4
-4.8	-4.8

Answer 1

Note: We are using SPSS software for alll our required statistical analysis

As per our given dataset is concerned, since the two groups are independent of each other, we are using Levene's F test for comparing the variances and Independent sample t test for testing the means

The hypothesis for our study would be

case 1: Testing variance

H₀: There is no significant difference in the variances between the two groups  

Vs

H₁: There is a significant difference in the variance between the two groups  

case 2: Testing Means

H₀: There is no significant difference in the means between the two groups  

Vs

H₁: There is a significant difference in the means between the two groups  

After entering the given data, we analyze the given output:

Interpretation:

As per the interpretation of SPSS is concerned,

if the significant value is greater than 0.05 (level of significance), we accept the Null Hypothesis and,

if the significant value is less than 0.05 (level of significance), we reject the Null Hypothesis

case 1:

In our case, we observe that, in case of the Levene's F Test, the significant value is 0.308, which is greater than 0.05. Hence, we accept the Null Hypothesis and claim that there is no significant difference in the variances of the scores between the two groups

case 2:

Again, we observe that, in case of the T Test, the significant values are 0.372 and 0.384, which is greater than 0.05. Hence, we accept the Null Hypothesis and claim that there is no significant difference in the means of the scores between the two groups