Construct a 95% Confidence Interval

Question

There were 50 students in session 1 of a STA 13 class last year (the total # of students was 519). In the final exam, the average score in session 1 was 56.3 and the standard deviation was 13.8. Construct a 95% confidence interval for the mean score of the whole STA class.

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Answer 1

Assuming a normal probability distribution, the standardized probability value, i.e. z value, that corresponds to 95% of the cumulative distribution is 1.96.

 

confidence interval (CI) = sample  mean - z value*SD/square root(n) , sample mean + z value*SD/square root(n) 

CI = 56.3 - 1.96*(13.8/sqrt(50)); 56.3 + 1.96*(13.8/sqrt(50))

CI = (52.5; 60.1)

 

what the above means is that 95% of the time a group of students take the STA 13 class out of the total 519, the mean score of the whole STA class will be between this interval and 5% of the time it will not.