Answer to Question #212799 in Statistics and Probability for Jhay

Question

B. (P-value Method). A teacher claims that more than 60% of the Grade 11 students preferred the use of the teacher-made video lessons as an alternative method in learning the Pre Calculus. In a survey of 200 students, 131 utilized the video lessons. Is there enough evidence to support the teacher's claim? Test the proportions at a-0.05.

Answer 1

$P=0.6$

$x=131$

$n=200$

$\hat P=\frac{131}{200}=0.655$

$H_0:P=0.6$

$H_a:P>0.6$

$z=\frac{\hat P-P}{\sqrt{\frac{P(1-P)}{n}}}$

$=\frac{0.655-0.6}{\sqrt{\frac{0.6\times 0.4}{200}}}$

$1.5877$

$z_{0.05}=1.645$

Since 1.5877<1.645, we fail to reject the null hypothesis. There is no sufficient evidence to support the teacher's claim that more than 60% of the Grade 11 students preferred the use of the teacher-made video lessons as an alternative method in learning the Pre-Calculus.