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Answer:
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group A is significantly lower than the mean for the group B.
Step-by-step explanation:
The statistic to test the hypothesis is given by this formula:
Where t follows a t distribution with degrees of freedom
The system of hypothesis on this case are:
Null hypothesis:
Alternative hypothesis:
Or equivalently:
Null hypothesis:
Alternative hypothesis:
Our notation on this case :
represent the sample size for group A
represent the sample size for group B
represent the sample mean for the group A
represent the sample mean for the group B
represent the sample standard deviation for group A
represent the sample standard deviation for group B
And now we can calculate the statistic:
Now we can calculate the degrees of freedom given by:
And now we can calculate the p value using the alternative hypothesis:
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group A is significantly lower than the mean for the group B.