Question

A fellow-student calculates a 99% confidence interval for a mean and gets (0.020,0.045). She says that there is a 99% chance that the true mean is between 0.020 and 0.045. Is she right? Why or why not?

Answer 1

Answer:

No. Once the confidence interval is calculated, the probability that it contains the true mean  is either 1 or 0. So then is not appropiate says that the confidence level is a chance. The best conclusion for this case would be:

We have 99% confidence that the true mean for the variable of interest on this case is between (0.02; 0.045)

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

$\bar X$ represent the sample mean for the sample  

$\mu$ population mean (variable of interest)  

s represent the sample standard deviation  

n represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:  

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)  

In order to calculate the mean and the sample deviation we can use the following formulas:  

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)  

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)  

After apply the procedure  we got that the interval is (0.02; 0.045) and we need to analyze if the following conclusion is right or no:

She says that there is a 99% chance that the true mean is between 0.020 and 0.045. Is she right? Why or why not?

The best answer for this case would be:

No. Once the confidence interval is calculated, the probability that it contains the true mean  is either 1 or 0. So then is not appropiate says that the confidence level is a chance. The best conclusion for this case would be:

We have 99% confidence that the true mean for the variable of interest on this case is between (0.02; 0.045)