Question

Two random samples are taken independently of one another and 90% confidence are calculated for each. If 10 is actually the true population mean, what is the probability that neither interval contains 10?  

Answer 1

Solution:

First we understand the meaning of 90% confidence interval.

The meaning of 90% confidence interval : 90% confidence interval means that there is 90% probability that the true population parameter will lie in the interval and 10% probability that the true population parameter will not lie in the interval

Now , in given example , two different and independent intervals are constructed using 90% level.

For each , P(Interval contains the true parameter) is 90% i.e. 0.90

P(Interval do not contains the true parameter) is 10% i.e. 0.10

Since two events are independent ,

P( neither interval contains 10 )

= P(neither Interval contains the true parameter)

= 0.10 * 0.10

= 0.01