the average height of females in the freshman class of certa

the average height of females in the freshman class of certain college has been 162.5 centimeters with a standard deviation of 6.9 centimeters. is there reason to believe that there has been a change in the average height if a random sample of 50 females in the present freshman class has an average height of 165.2 centimeters? use a 0.05 level of significance

Solution

The test hypothesis is
Ho:=162.5
Ha: not equal to 162.5

The test statistic is

Z=(xbar-)/(s/n)

=(165.2-162.5)/(6.9/sqrt(50))

= 2.77

P-value = 2*P(Z>2.77)=0.0056 (check standard normal table)

Since the p-value=0.0056 is less than 0.01, we reject Ho.

So we can conclude that there has been a change in the average height if a random sample of 50 females in the present freshman class has an average height of 165.2 centimeters