Question

Even more tall girls, Refer to Exercises $12$and $14$. Suppose that the sample mean height of the twenty $16$-year-old females is $\overline{x}=65.8$inches. Would this sample mean provide convincing evidence that the average height of all $16$-year-old females at this school is greater than $64$inches? Explain your reasoning.

Short answer

It would be remarkable to acquire a sample mean of $\overline{x}=65.8$or larger in an SRS of size $20$from a normal population with $\mu =64$inches, because none of the values of $\overline{x}$were $65.8$ inches or greater. As a result, a sample mean of $\overline{x}=65.8$inches provides convincing evidence

Step-by-step solution

Given information 

We have been given that the sample mean height of the twenty $16$-year-old females is $\overline{x}=65.8$inches.

Explanation

It would be remarkable to acquire a sample mean of $\overline{x}=65.8$or larger in an SRS of size $20$from a normal population with $\mu =64$inches and $\sigma =2.5$inches, because none of the values of $\overline{x}$were $65.8$inches or greater. As a result, a sample mean of $\overline{x}=65.8$inches provides convincing evidence that the $16$-year-old females population mean height is more than $64$inches. The disparity between the sample mean ($\overline{x}=65.8$) and the mean indicated by the National Center for Health Statistics ($\mu =64$) cannot be explained by sampling variability.