The average height of females in the freshman class of a certain college has historically 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 p-value in your conclusion. assume the standard deviation remains the same.

Step-by-step explanation:

Let X be the average height of females in the freshman class.

X is N(162.5, 6.9)

Sample mean = 165.2

Sample size = 50

Since population std deviation is known and n >30 we can use z statistic

Z = (x bar-mu)/Sigma/sqrt n

i.e. Z =

=2.766

Let alpha be 5%

Z critical value for 95% is 1.96

Our test statistic >1.96

p value = 0.001<0.05(our alpha)

Hence reject null hypothesis

The sample mean > the population mean

Alternate hypothesis is true.

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