Imagine a class of twentyfive 12yearold girls with an averag

Imagine a class of twenty-five 12-year-old girls with an average height of 62 inches. We know that the population mean and standard deviation for this age group of girls is m=59 inches, s = 2.5 inches. (Note that this is a z statistic problem.)

A- Calculate the z statistic for this sample.

B- How does this sample mean compare to the distribution of sample means? In other words, how does the height of the girls in the sample compare to the height of girls in the general population?

Solution

Set Up Hypothesis
Null Hypothesis H0: U=62
Alternate Hypothesis H1: U!=62
Test Statistic
Population Mean(U)=62
Given That X(Mean)=59
Standard Deviation(S.D)=2.5
Number (n)=25
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=59-62/(2.5/Sqrt(25)
Zo =-6
| Zo | =6
Critical Value
The Value of |Z a| at LOS 0.03% is 1.88
We got |Zo| =6 & | Z a | =1.88
Make Decision
Hence Value of | Zo | > | Z a| and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -6 ) = 0
Hence Value of P0.03 > 0, Here we Reject Ho

height of the girls in the sample is diffrent from population