Help me solve this question please.

Question

The heights of male students in a college are thought to be normally distributed with mean 170 cm and standard deviation 7.

The heights of 5 male students from this college are measured and the sample mean was 174 cm.

Determine, at 5% level of significance, whether there is evidence that the mean height of the male students of this college is higher than 170 cm

Answer 1

This is an example of a one-sample z-test. You have a population mean of mu = 170 cm. and standard deviation of sigma = 7 cm. You are then comparing one sample of N = 5 with a mean of xbar = 174 cm to this population. The equation for the one-sample z-test is:

(xbar - mu)/(√sigma/N) or in this case:

z = (174 - 170)/(7/√5)

Once you have this, you must compare this to a critical z-value. Because we are only interested in determining if heights are higher, this is a one-tailed test.

Here is a website to look up critical values

https://www.graphpad.com/quickcalcs/statratio1/

You choose the "z-ratio" and .05 for the "probability." This will give you the correct critical value. Be sure you use the one-tailed one (it will be smaller).

If the Z you calculated above is larger than this critical value, you can conclude, "there is evidence that the mean height of the male students of this college is higher than 170 cm." If not, there is NOT evidence that the mean height is higher.

I hope that is helpful!

Dr. Jenny