Answer to Question #235841 in Statistics and Probability for Jope

Question

A lecturer wants to know if his statistics class has a good grasp of basic maths from matric
level. Eleven students are chosen at random from the class and given a maths proficiency test.
The lecturer wants the class to be able to score above 75 on the test to show that they had a
good grasp of basic maths. The eleven students get scores shown below:
62 88 71 50 67 70 92 75 68 83 95
Can the lecturer be 95 percent confident that the students had a good grasp of basic
maths? (20 marks)

Answer 1

We need to construct 95% CI and if 75 is within the interval, we conclude that there is no sufficient evidence to support the claim that the students had a good grasp of basic math. Let's assume the data come from a normally distributed population.

$CI=\bar X\pm t_{n-1,\frac{\alpha}{2}}\frac{s}{\sqrt{n}}$

$\bar X=74.636$

$s=13.669$

$n=11$

$\alpha=0.05$

$t_{10,0.025}=2.228$

$95\% CI=74.636\pm 2.228\times\frac{13.669}{\sqrt{11}}$

$=74.636\pm9.1833$

= [65.45,83.82]

Since 75 is within the interval, there is no sufficient evidence to conclude that the students had a good grasp of basic math. The lecturer cannot be be 95 percent confident that the students had a good grasp of basic math.