Answer to Question #326895 in Statistics and Probability for arron

Question

1. A DepEd official claim that the average performance in Mathematics is 82.4%. A random of 25 students showed that their mean performance in Mathematics is 81.3% with a standard deviation of 4.2%. Test whether the mean performance of the students is not significantly lower than the general average. Use 0.01 level of significance.

Answer 1

t-value for 24 degrees of freedom (less by one than the number of students) and 0.01 level of significance is 2.492

Let $\mu=81.3\%,\space\sigma=4.2\%,\space n=25$

With given significance level real mean is lower than $\mu+t_{24}\frac{\sigma}{\sqrt{n}}=81.3\%+2.492\cdot\frac{4.2\%}{\sqrt{25}}\approx83.4\%$

82.4% < 83.4%, => mean is not significantly lower than the general average