Answer to Question #267093 in Statistics and Probability for Yabona

Question

A lecturer wants to know if his introductory statistics class has a good grasp of basic maths done at matric level. The student’s understanding would help the lecturer to plan for the courses to be undertaken. Nine students were chosen at random from the class and given a maths proficiency test. The lecturer wants the class to be able to score at least 70 on the test to show a good grasp of basic maths. The selected nine students get scores of 92, 75, 85, 68, 58, 60, 83, 95 and 57. Use the p-value approach to find out whether the mean score for the class on the test would be at least 70 at an alpha of 1%? 

Answer 1

H_o : $\mu$_o = 70

vs

H_a : $\mu$_o > 70

From the sample;

$\bar{X}$ = 74.7778

S = 14.7460

The observed value of the test statistic t is given by;

t = $\frac{\bar{x}-\mu\omicron}{s/\sqrt{n}}$

= $\frac{74.7778-70}{\sqrt{9}}$

= 0.9720.

Degrees of freedom = n - 1 = 9-1 = 8.

Using excel, p- value = 0.179759. formula: =tdist(x, df, tail)

=tdist(0.9720, 8, 1)

Conclusion : Since the p- value = 0.179759 > $\alpha$ =0.01, we fail to reject H_O at 1 % level of significance and conclude that there is no sufficient evidence to indicate that the true mean score for the class would be at least 70.