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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 FAIL to reject the null hypothesis, and we can said that at 1% of significance the mean for the control group it's not significantly higher than the mean of the treatment group by 1 point.
Step-by-step explanation:
When we have two independent samples from two normal distributions with equal variances we are assuming that
And the statistic is given by this formula:
Where z follows a normal standard distribution
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 control
represent the sample size for group treatment
represent the sample mean for the group control
represent the sample mean for the group treatment
And now we can calculate the statistic:
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 FAIL to reject the null hypothesis, and we can said that at 1% of significance the mean for the control group it's not significantly higher than the mean of the treatment group by 1 point.