Answer to Question #180164 in Statistics and Probability for Francis

Question

The Head of the Math Department announced that the mean score of Grade 9 students in the first periodic examination in Mathematics was 89 and the standard deviation was 12. One student 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. At 0.01 level of significance, test the student’s belief.

Answer 1

$H_0:\mu=89.$

$H_a:\mu<89.$

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

P-value: $p=P(Z<-1.94)=0.0262.$

Since the P-value is greater than 0.01, fail to reject the null hypothesis.

There is no significant evidence that the mean score is less than 89.