Answer:
The degreess of freedom are given by:
Now we can calculate the p value with the following probability:
For this case since the p value is higher than the significance level we can FAIL to reject the null hypothesis and we can conclude that the true means are NOT significantly different at 10% of significance.
Step-by-step explanation:
Information provided
represent the mean for sample 1
represent the mean for sample 2
represent the sample standard deviation for 1
represent the sample standard deviation for 2
sample size for the group 2
sample size for the group 2
Significance level provided
t would represent the statistic
Hypothesis to test
We want to verify if the true means for this case are significantly different, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
And the degrees of freedom are given by
Replacing the info given we got:
The degreess of freedom are given by:
Now we can calculate the p value with the following probability:
For this case since the p value is higher than the significance level we can FAIL to reject the null hypothesis and we can conclude that the true means are NOT significantly different at 10% of significance.