A study reports that recent college graduates from New Hampshire face the highes

Question

A study reports that recent college graduates from New Hampshire face the highest average debt of $31,486 (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 below. Assume that the population standard deviation is $5,000. Use Table 1.

Use Excel to 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.)

Use the 95% confidence interval to determine if the debt of Connecticut undergraduates differs from that of New Hampshire undergraduates.

A study reports that recent college graduates from New Hampshire face the highest average debt of $31,486 (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 below. Assume that the population standard deviation is $5,000. Use Table 1.

Explanation / Answer

here mean dept of connecticut students =24436.48

and std errror =std deviation/(n)1/2=5000/(40)1/2=790.57

for 95% CI, z =1.96

hence confidence interval=mean+/- z*std error =22886.96 ; 25985.99

b)The debt of Connecticut undergraduates differs from that of New Hampshire undergraduates. as our confidence interval does not contain 31486 as possible interval value.

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