Answer:
Since we conduct a bilateral test we have the p value given by:
Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true means for girls and boys are different at 1% of significance
Explanation:
Information given
represent the mean weigth for ten year boys
represent the mean weigth for ten year girls
represent the sample deviation for 10 year boys
represent the sample standard deviation for 10 year girls
sample size for boys
sample size for girls
t would represent the statistic
significance level assumed
System of hypothesis to check
We need to conduct a hypothesis in order to check if the true means are different for boys and girls, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic for this case would be given by:
(1)
Replacing we got:
P value
We can assume that the degrees of freedom for this case are large enough to assume that the t distribution is approximately the normal distribution.
Since we conduct a bilateral test we have the p value given by:
Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true means for girls and boys are different at 1% of significance