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Chapter 7: Q. 16 (page 456)

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

Short Answer

Expert verified

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

Step by step solution

01

Given information 

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

02

Explanation

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

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