Answer to Question #323761 in Statistics and Probability for infinity

Question

A math teacher believes that a grade 7 student will get a score of not more than 70 in the 100-item diagnostic test administered last week. To test this claim, the scores of 40 students who took the diagnostic test was recorded. The mean of their scores is 87.65 with a standard deviation of 6. Which of the following test statistic should be used?

Answer 1

$T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{40}\frac{87.65-70}{6}=18.6047\sim t_{n-1}=t_{39}\\One-tail\,\,test$