How would i solve this using statistics

People who use Lifelocker when perform financial operations online tent to be more secure rather than people who don’t use Lifelocker. Based on our data sample of 40 online users, 20 users out of the total data sample have used LifeLoker. Those 20 online users have not experience identity theft prior to purchasing LifeLocker credit protection. However, 15 individuals out of the remaining 50% of users have encountered some form identity theft.

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As this is a between subjects design with two groups, those who have used Lifelocker (1) and those who have not used life locker (2), and one dependent variable, experienced identity theft (It), you can use a simple t-test to compare group means. We will use the independent two-sample t-test. The assumptions of this test are that the number of data points in each group is the same (true in our case), and that the variance is the same for both groups. We can assume the latter because there is no reason to believe that the people who compose group 1 are somehow fundamentally differently on some unrelated variable compared to those who compose group 2:

Mean of group 1 (`X_1` ) = 0

Mean of group 2 (`X_2` ) = 0.75

`X_1-X_2=-0.75`

Standard deviation of group 1 (`S_(X_1)` )= 0

Standard deviation of group 2 (`S_(X_2)` )= 0.444262

`S_(X_1X_2)=sqrt(1/2(S_(X_1)^2+S_(X_2)^2))=0.31414`

`n = 20 -gt sqrt(2/n)= 0.316228`

`t=(X_1-X_2)/(S_(X_1X_2)*sqrt(2/n))=-7.54983`

Looking up this value in a t-table for 20 subjects, our value is indicative of a very high significant difference between group 1 and group 2 with p<<0.01.

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