A recent study found that consumers are making average monthly debt payments of

Question

A recent study found that consumers are making average monthly debt payments of $983 (Experian.com, November 11, 2010). The accompanying table shows a portion of average debt payments for 26 metropolitan areas. Use Table 2.

  City

Debt Payments

  Washington, D.C.

$1,285         

  Seattle

1,135         

  Baltimore

            1,133         

  Boston

1,133         

  Denver

1,104         

  San Francisco

1,098         

  San Diego

1,076         

  Sacramento

1,045         

  Los Angeles

        1,024         

  Chicago

1,017         

  Philadelphia

1,011         

  Minneapolis

   1,011         

  New York

  989         

  Atlanta

986         

  Dallas

970         

  Phoenix

957         

  Portland

948         

  Cincinnati

920         

  Houston

889         

  Columbus

888         

  St. Louis

886         

  Miami

867         

  Detroit

832         

  Cleveland

812         

  Tampa

791         

  Pittsburgh

763         

SOURCE: http://www.Experian.com, November 11, 2010.

Click here for the Excel Data File

a.

Use Excel to calculate the mean and standard deviation for debt payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

  Sample mean

  Sample standard deviation

b.

Construct a 90% and a 95% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)

  Confidence Level

Confidence Interval

90%

to

95%

to

A recent study found that consumers are making average monthly debt payments of $983 (Experian.com, November 11, 2010). The accompanying table shows a portion of average debt payments for 26 metropolitan areas. Use Table 2.

Explanation / Answer

Answer:

a) Mean= SUM/n= 25570/26= 983.46

Standard deviation = 124.61 ( By using excel function STDEV)

b) M = 983.4615

t = 1.71
sM = ?(124.60862/26) = 24.44

? = M ± t(sM)
? = 983.4615 ± 1.71*24.44
? = 983.4615 ± 41.743129

M = 983.4615, 90% CI [941.718371, 1025.204629].

You can be 90% confident that the population mean (?) falls between 941.72 and 1025.20.

M = 983.4615

t = 2.06
sM = ?(124.60862/26) = 24.44

? = M ± t(sM)
? = 983.4615 ± 2.06*24.44
? = 983.4615 ± 50.330503

M = 983.4615, 95% CI [933.130997, 1033.792003].

You can be 95% confident that the population mean (?) falls between 933.13 and 1033.79

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