The National Health Statistics Reports published in 2018 reported that a sample of 360 ten-year old boys had a mean weight of 70.5 pounds with a standard deviation of 5.3 pounds. In addition a sample of 329 ten-year-old girls had a mean weight of 68.7 pounds with a standard deviation of 4.3 pounds. Can you conclude that the mean weights of ten-year-old boys and girls differ? Use = 0.01.

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

Step-by-step 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

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step-by-step explanation: