Each student was asked to record and report the amount of money they spent on text books in a semester. The sample of 130 students resulted in the average of $422 and a standard deviation of $57. Find a 99% confidence interval for the mean amount of money spent by collage students on textbooks

(409.36, 434.64)

Step-by-step explanation:

When population standard deviation is unknown and sample is not so large , then the formula to find the confidence interval for population mean is given by :-

, where = sample mean , n = sample size , s= sample population standard deviation, t*= two tailed critical value.

As , per given , , s=$57, n=130

For 99% confidence ,

By t-distribution table , t-value for   (two tailed) and df =129 [∵df=n-1] would be

t*=2.6145

Now , the  99% confidence interval for the mean amount of money spent by collage students on textbooks will be :

Hence, a 99% confidence interval for the mean amount of money spent by collage students on textbooks will be (409.36,  434.64).