Question

The University of Avalon (U of A) wants to know how much credit card debt students typically have when they graduate. A survey of 32 recent graduates indicated that the mean debt was 2430 pounds with a standard deviation of 1850 pounds. Find a 99% confidence interval for the average credit card debt for all recent U of A graduates. Assume the credit card debt is normally distributed.  

Round answers to 2 decimal places.

Use the tables in the book and not an outside source.

Please show work for the opportunity to earn partial credit on this question.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 2430

sample standard deviation = s = 1850

sample size = n = 32

Degrees of freedom = df = n - 1 = 32 - 1 = 31

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t0.005,31 = 2.744

Margin of error = E = t/2,df * (s /n)

= 2.744 * ( 1850 / 32 )

Margin of error = E = 897.39

The 99% confidence interval estimate of the population mean is,

  ± E  

= 2430 ± 897.39

= ( 1532.61, 3327.39 )