Question 1199107
the sample size is 40
the sample mean is 60000.
the sample standard deviation is 7500.


you would use the t-score to help solve this.
the formula is t = (x-m)/s
t is the t-score
x is the sample mean
m is the population mean
s is the standard error.


the standard error is equal to the standard deviation / square root of sample size = 7500 / sqrt(40) = 1185.854123.


at 99% confidence interval, you would calculate the two-tailed critical t-score with 39 degrees of freedom (sample size minus 1) to be plus or minus 2.707913179.


on the high side of the confidence interval, your t-score formula becomes:
2.707913179 = (60000 - m) / 1185.854123.
your margin of error on the high side is equal to (60000 - m) which is equal to 2.707913179 * 1185.854123 = 3211.190008.
this indicates that your mean is 60000 - 3211.190008 = 56788.80999.


your solution should be:


Part a) What is the error bound/margin E in our prediction about μ?
margin of error = 3211.19 rounded to 2 decimal places.


Part b) What prediction do we make about μ?
population mean is assumed to be 56788.81 rounded to 2 decimal places.