The average grade in Math 1530 on test 3 has always been 75

The average grade in Math 1530 on test 3 has always been 75. This semester, the average grade on test 3 for 15 students in 1530 was 77.5 with a standard deviation of 5.51. At alpha = 0.10, has the average grade changed for the 3rd test in 1530?

Solution

Let mu be the population mean

The test hypothesis:

Ho: mu=75 (i.e. null hypothesis)

Ha: mu not equal to 75 (i.e. alternative hypothesis)

The test statisitc is

t=(xbar-mu)/(s/vn)

=(77.5-75)/(5.51/sqrt(15))

=1.757

It is a two-tailed test.

The degree of freedom =n-1=15-1=14

Given a=0.1, the critical values are t(0.05, df=14) =-1.76 or 1.76 (from student t table)

The rejection regions are if t<-1.76 or t>1.76, we reject the null hypothesis.

Since t=1.757 is between -1.76 and 1.76, we do not reject the null hypothesis.

So we can not conclude that the average grade has changed for the 3rd test in 1530