Question

5. TWO (INDEPENDENT) SAMPLE T-TEST

(a) Describe the independent samples t-test for two means briefly. How does it do it? (b) State the null and the alternative hypothesis. (c) State the assumptions. (d) State the formula for the test statistic. (e) State the rejection rule with (How to reject the null hypothesis) (f) Give an real life example of how we can use the independent samples t-test for two means.

Answer 1

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0
......

Sample #1   ---->
mean of sample 1,    x̅1
standard deviation of sample 1,   s1
size of sample 1,    n1
  
Sample #2   ---->
mean of sample 2,    x̅2
standard deviation of sample 2,   s2
size of sample 2,    n2
  
difference in sample means =    x̅1-x̅2
  
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2))   
std error , SE =    Sp*√(1/n1+1/n2)
  
t-statistic = ((x̅1-x̅2)-µd)/SE  

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rejection rule :

if test stat > critical value

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assumption:

1. The data are continuous (not discrete).
2. The data follow the normal probability distribution.
3. The variances of the two populations are equal.
4. The two samples are independent. There is no relationship between the individuals in one sample as
compared to the other (as there is in the paired t-test).
5. Both samples are simple random samples from their respective populations. Each individual in the
population has an equal probability of being selected in the sample

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