Student grades often have a normal distribution In a very la

Student grades often have a normal distribution. In a very large class of 500, you and 4 other friends would like to see how your scores match up to the class average of 70 points. The five scores are: 99, 60, 87, 94, and 83. Is there a significant difference between your five scores and the scores of your overall class?

Solution

sample sizn n=5

sample mean =84.6

sample standard deviation =15.07647

The test hypothesis:

Ho: mu=70 (i.e. null hypothesis)

Ha: mu not equal to 70 (i.e. alternative hypothesis)

The test statistic is

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

=(84.6-70)/(15.07647/sqrt(5))

=2.17

It is a two-tailed test.

The degree of freedom =n-1=5-1=4

Assume that the significant level a=0.05

The critical values are t(0.025, df=4) =-2.78 or 2.78 (from student t table)

The rejection regions if t<-2.78 or t>2.78, we reject the null hypothesis.

Since t=2.17 is between -2.78 and 2.78, we do not reject the null hypothesis.

So we can not conclude that there is a significant difference between your five scores and the scores of your overall class