Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.

We can say at 99% confidence that the true mean is between (91.674;98.326)    

Step-by-step explanation:

Data given

represent the sample mean

population mean (variable of interest)

s=6.6 represent the sample standard deviation

n=30 represent the sample size  

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

  (1)

We need to find the critical value and we need to find first the degrees of freedom, given by:

Since the Confidence is 0.99 or 99%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,29)".And we see that

And replacing we got:

We can say at 99% confidence that the true mean is between (91.674;98.326)