suppost we wanted to test the hypothesis that control a group of cancer patients(group 1) would report higher mean pain ratings than an experimental group recieving special message treatment(group 2). Use the following information, Compute at a t-statistice for independent group;
mean group 1=78.5 s(square/1)=42.1 and n(1)=25
mean group 2=72.1 s(square2/2)=39.7 and n(2) =25
Use an independent groups t-test for your two samples. n1 + n2 - 2 degrees of freedom is used for this test. Use a t-table to determine your cutoff or critical value to reject the null (you should have a significance level set for the test). If your test statistic exceeds the critical value from the table, reject the null and conclude a difference. If the test statistic does not exceed the critical value from the table, do not reject the null. You cannot conclude a difference in this case.
I hope this will give you a few hints to get started on your problem.
To compute the t-statistic for independent groups, you can follow these steps:
Step 1: State the null and alternative hypothesis.
In this scenario, the null hypothesis (H0) would be that there is no significant difference in mean pain ratings between the control group (group 1) and the experimental group receiving special message treatment (group 2). The alternative hypothesis (Ha) would be that the mean pain ratings in group 1 are higher than in group 2.
Step 2: Calculate the standard error (SE) for the difference in means.
The formula for the standard error is as follows:
SE = sqrt((s1^2 / n1) + (s2^2 / n2))
where s1^2 is the variance of group 1, n1 is the sample size of group 1, s2^2 is the variance of group 2, and n2 is the sample size of group 2.
Given the values:
s1^2 = 42.1, n1 = 25
s2^2 = 39.7, n2 = 25
Calculating the standard error:
SE = sqrt((42.1 / 25) + (39.7 / 25))
Step 3: Calculate the t-statistic.
The formula for the t-statistic for independent groups is:
t = (x1 - x2) / SE
where x1 is the mean of group 1, x2 is the mean of group 2, and SE is the standard error calculated in the previous step.
Given the values:
x1 = 78.5
x2 = 72.1
SE (calculated in Step 2) = ...
Calculating the t-statistic:
t = (78.5 - 72.1) / SE
By plugging in the values and performing the calculation, you can obtain the t-statistic.