Question

A study reports that recent college graduates from New Hampshire face the highest average debt of $31,321 (The Boston Globe, May 27, 2012). A researcher from Connecticut wants to determine how recent undergraduates from that state fare. He collects data on debt from 40 recent undergraduates. A portion of the data is shown in the accompanying table. Assume that the population standard deviation is $5,300. [You may find it useful to reference the z table.] Debt 24, 044 19,150 26,759 31,920 31,533 34,211 14,623 24,366 31,020 20, 110 22,088 17,093 16,301 20,658 21,672 14,955 22,696 21,675 14,952 22,705 Debt 23,520 26,214 23,718 24,036 19,159 26,764 31,921 31,531 34,212 14,629 29,866 37,413 22,269 30,048 35, 131 25, 117 22,924 28,916 23,636 29,324 picture Click here for the Excel Data File a. Construct the 95% confidence interval for the mean debt of all undergraduates from Connecticut. (Do not round intermediate calculations. Round "z" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval b. Use the 95% confidence interval to determine if the debt of Connecticut undergraduates differs from that of New Hampshire undergraduates. The debt of Connecticut undergraduates differs from that of New Hampshire undergraduates. The debt of Connecticut undergraduates does not differ from that of New Hampshire undergraduates.

Answer 1

Answer:

n	40
mean	24821.9750

Z value for 95% = 1.960

σ =5300

$CI = \bar x \pm z *\frac{\sigma}{\sqrt{n}}$

$CI = 24821.9750 \pm 1.960*\frac{5300}{\sqrt{40}}$

=( 23179.52, 26464.43)

Confidence interval   = 23179.52 to 26464.43

b).

The debt of Connecticut undergraduates differs from that of New Hampshire undergraduates.

( note: The value 31321 does not contain in the interval ( 23179.52, 26464.43) )