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Answer:
Since the p value is higher than the significance level given of 0.01 we don't have enough evidence to conclude that the true mean for group 1 is significantly higher thn the true mean for the group 2.
Step-by-step explanation:
Data given
represent the sample size for group 1
represent the sample size for group 2
represent the sample mean for the group 1
represent the sample mean for the group 2
represent the sample standard deviation for group 1
represent the sample standard deviation for group 2
System of hypothesis
The system of hypothesis on this case are:
Null hypothesis:
Alternative hypothesis:
We are assuming that the population variances for each group are the same
The statistic for this case is given by:
The pooled variance is:
We can find the pooled variance:
And the pooled deviation is:
The statistic is given by:
The degrees of freedom are given by:
The p value is given by:
Since the p value is higher than the significance level given of 0.01 we don't have enough evidence to conclude that the true mean for group 1 is significantly higher thn the true mean for the group 2.