Answer:
For this case the confidence interval for the differences of the true means is given by:
With the degrees of freedom given by:
And for this case the confidence interval for the true difference of means is given by:
So then we have enough evidence to conclude that the true means are different and one of the two is significantly higher than the other one. So then the claim makes sense at 10% of significance.
Step-by-step explanation:
Assumptions
For this case we assume that we have the following info given :
the sample mean for the group 1
the sample mean for the group 2
the sample deviation for the group 1
the sample deviation for the group 2
represent the sample size for 1
represent the sample size for 2
Solution to the problem
For this case the confidence interval for the differences of the true means is given by:
With the degrees of freedom given by:
And for this case the confidence interval for the true difference of means is given by:
So then we have enough evidence to conclude that the true means are different and one of the two is significantly higher than the other one. So then the claim makes sense at 10% of significance.