Answer to Question #217876 in Statistics and Probability for Monica

Question

assistant principal of the Senior High School Department announced that the mean score of Grade 11 students in the first quarter examination in Statistics was 89 and the standard deviation was 12. One teacher who believed that the mean score was less than this, randomly selected 34 students and computed their mean score. She obtained a mean score of 85.

Answer 1

$\text{Null Hypothesis }H_0:\mu=89.$

$\text{Alternate Hypothesis }H_a:\mu<89.$

Test statistic: $z=\dfrac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}=\dfrac{85-89}{\frac{12}{\sqrt{34}}}=-1.94.$

P-value: $p=P(Z<-1.94)=0.0262.\$

Here, we can analyze that the P-value is greater than 0.01 So, it fails to reject the null hypothesis.

Hence, there is no significant evidence that the mean score is less than 89.