Question #229017

1.2 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? 


1
Expert's answer
2021-08-28T01:36:18-0400

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=Xˉ±tn1,α2snCI=\bar X\pm t_{n-1,\frac{\alpha}{2}}\frac{s}{\sqrt{n}}

Xˉ=74.636\bar X=74.636

s=13.669s=13.669

n=11n=11

α=0.05\alpha=0.05

t10,0.025=2.228t_{10,0.025}=2.228

95%CI=74.636±2.228×13.6691195\% CI=74.636\pm 2.228\times\frac{13.669}{\sqrt{11}}

=74.636±9.1833=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.


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