Final answer:
To test the claim that boys and girls have the same mean length of stay, a hypothesis test can be conducted using a t-test to compare the means of two independent groups (boys and girls) at the 5 percent level of significance.
Step-by-step explanation:
In order to test the claim that boys and girls have the same mean length of stay, a hypothesis test can be conducted. The null hypothesis is that the mean length of stay for boys and girls is the same, while the alternative hypothesis (Ha) is that the mean length of stay is different between boys and girls.
Using the given information, a t-test can be performed to compare the means of two independent groups (boys and girls). The test should be conducted at the 5 percent level of significance, which means that the p-value should be less than 0.05 to reject the null hypothesis.
If the p-value is less than 0.05, there is sufficient evidence to conclude that the mean length of stay for boys and girls is different. If the p-value is greater than or equal to 0.05, there is not enough evidence to conclude a difference in means.