Question

Lacey is interested in determining whether people who have experienced a traumatic event experience more sleep disturbances than people who have not experienced such an event. She distributes a sleep disturbance survey to 103 individuals wh o experienced a traumatic event and to 98 people who had never experienced a traumatic event. If the mean score on the survey was 13.20 ( s = 3.51) for the trauma group and 8.10 ( s = 2.17 ) for the non-trauma group, what test should Lacey conduct and what would the results of that test indicate? (Assume that higher scores indicate more disturbances).

Answer 1

Since here are the two groups. One experienced trauma and other one never experienced trauma.

We can use T test for independent. Let us assume that two populations have equal variance.

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS HA:

So pooled variance will be

sp^2= (n1-1)*s1^2+(n2-1)*s2^2/n1+n2-2

s1​=3.51 , n1​=103 , s2​=2.17 and n2​=98

Plugging in the corresponding values in the formula above, we get that

sp^2​=(103−1)(3.51)^2+(98−1)(2.17)^2​/(103+98−2)=8.6101

Now that we have the pooled variance, we can compute the pooled standard deviation by simply taking the squared root of the value obtained for the variance.

The following pooled standard deviation is obtained:

sp​=sqrt(8.6101)​=2.9343

alpha= 0.05 (We assume level of significance is 0.05)

P value= 0.00000

P value<0.05 which is significant.

Since P value is significant Reject null hypothesis and we can conclude that more sleeping distrbance experienced by people who have experience trauma.