Question: When should a researcher use a z test compared to one sample t test? in other words what circumstances is each test considered appropriate? The dean of the school of science dept. is interested in finding out if facility in the psychology dept. publish at different rates than the national average of 8 publication for every 10 years. a random sample of size 5 was taken from academic staff. the data obtained were: 3, 21, 1, 15 and 7 the sample mean is 9.4 standard deviation is 8.41 is the sample mean of 9.4 publication for science facility at school is significantly different than the national average of 8 state both null and alternative hypothesis in symbols and words test your hypothesis (alpha=.05)?