Quote:
Originally Posted by mwe  The following data values are a simple random sample from a population that’s normally distributed, with σ2 = 4.0 11, 6, 8, 12, and 13. Construct and interpret the 90% and 95% confidence intervals for the population mean. show solution pls.. |
Sorry, we do not solve the problem for you - that is your job.
However, I will get you started:
For any confidence interval, call value of the confidence level
(such as 90% or 95%, as in your case). Then the probability that the true population mean (called
) lies within a given interval with a confidence level of
is:
where
are your mean, z-score, standard deviation, and sample size, respectively.
So your confidence interval is between the points
To find a given confidence interval, plug in those values. The z-score will be based on your confidence level. Look them up in a z-table. A 90% confidence interval will exclude 5% of the normal distribution on neither side (a total of 10% excluded). A 95% confidence interval will exclude 2.5% (for a total of 5% excluded).
In other words, for a 90% confidence interval, you say with repeated experiments using the same z-score, sample size, and standard deviation, the true population mean will fall within your intervals 90% of the time.