A principal of Eclipse High School wants to know if his stud

A principal of Eclipse High School wants to know if his students\' maths performance is better than the national average of 70%. Of the 200 students he to took a sample of twelve (12). Their exam scores are shown below:

Solution

The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: ? = 70 %
Alternative hypothesis: ? ? 70 %

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

For this analysis, the significance level is 0.05.

Here u = 70

n is the sample students 12

s is the standard deviation of the sample 13.4377

x is the sample mean 76.25

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t-score test statistic (t).

SE = s / sqrt(n) = 13.4377 / sqrt(12) = 3.879

DF = n - 1 = 12 - 1 = 11

t = (x - ?) / SE = (76.25