Another teacher decides to average the height of all 15yearo

Another teacher decides to average the height of all 15-year-old male students in his classes throughout the day. By the end of the day, he has measured the heights of 57 boys and calculated an average of 68.1 inches. (population mean: 67in, standard deviation:3.19in)

a. calculate the mean and the stadard error of the distribution of mean heights.

b. calculate the z statistic for this group.

c. what percentage of groups of people would we expect to have mean heighs, based on samples of this size (57), taller than this group?

d. How often do mean heights equal to or more extreme than 68.1 occur in this population?

e. How does this result compare to the statisical significance cutoff of 5%?

Solution

a) E(xbar)=67

se(xbar)=sd/sqrt(n)=0.4225

b) z=xbar-mu/se=68.1-67/0.4225=2.6033

c) use NORM.DIST(68.1,67,0.4225,true) in excel and subtract with 1, we get 0.004613 so 0.4613%

d) Since this is a normal distirbution and mean is 68.1 the probability of any value gretaer than or equal to the mean is 0.5

e) finding 95% confidence interval we get (67.27,68.92).