Question

A local school district claims that the number of school days missed by its teachers due to illness is below the national average of 5 with a population standard deviation of 2.119. A random sample of 40 teachers provided the data below. Test the district's claim using a=0.05. Show graph.

0	3	6	3	3	5	4	1	3	5
7	3	1	2	3	3	2	4	1	6
2	5	2	8	3	1	2	5	4	1
1	1	2	1	5	7	5	4	9	3

Answer 1

For the given random sample

mean=sum of total number/ total sample

mean=(0+3+6+3+....4++9+3)/40=3.4

population mean=5

standard deviation of population=2.119

H0 :u>=5

H1:u<5

z=(3.4-5)/[2.119/sqrt(40)]=-4.77

Z at aplha =0.05= should lies between -1.96 and +1.96 from Z table

therefore z calculated i.e -4.77 is less than-1.96 reject the null hypothesis.