A study of 25 graduates of four-year public colleges revealed the mean amount owed by a student in student loans was $55,051. The standard deviation of the sample was $7,568. Required:
a. Construct a 90% confidence interval for the population mean.
b. Confidence interval for the population men between up to

a

   The  90%  confidence interval is  

b

Confidence interval for the population men between $52561.13  up to $57540.8

Step-by-step explanation:

From the question we are told that

   The sample size is  

     The  sample mean is  

     The standard deviation is  

Given that the confidence level is  90% then the level of confidence is mathematically represented as

Next we obtain the critical value of from the normal distribution table the values is  

Generally the margin of error is mathematically  represented as

substituting values

The 90% confidence interval is mathematically evaluated as

substituting values

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680