Question

Suppose that a 96% confidence interval for the population mean grade (in percentage) of all Stat 4800 students at Langara College is (65.6, 70.2). Explain why the following definition of this interval is wrong: “96% of all Langara students have grades that are between 65.6 and 70.2”.

Answer 1

Solution:

Given ,

96% confidence interval for the population mean is  (65.6, 70.2)

The meaning of 96% confidence interval : 96% confidence interval means that there is 96% probability that the true population parameter will lie in the interval.

If we draw several samples of size n and we constructed the 96% confidence intervals using these samples , then 96% of these intervals will contain the true population parameter and 4% intervals will not contain the true population parameter.

It does not mean that  “96% of all Langara students have grades that are between the interval"