A recent study found that consumers are making average monthly debt payments of
ID: 3229643 • Letter: A
Question
A recent study found that consumers are making average monthly debt payments of $983 (Experian.com, November 11, 2010). The table (Debt_Payments.xls) shows a portion of average debt payments for 26 metropolitan areas.
a) State the null and the alternative hypothesis in order to test whether average debt payments are greater than $900.
b) What assumption regarding the population is necessary to implement the step?
c) Calculate the value of the test statistics.
d) Calculate the p-value.
e) Use a p-value approach to make a decision at 5% level of significance.
(Debt_Payments.xls) here is excel sheet data
Metropolitan area 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 763Explanation / Answer
null hypothesis: mean =900
alternate hypothesis: mean>900
b)assumption requierd is that data follows normal distribution as well sample is random
c)
from above value of test stat t=3.4153
d) p value =0.0011
e) as p value is less then 0.05 ; we reject null hypothesis and conclude that average debt payments are greater than $900
X Washington, D.C. 1285 Seattle 1135 Baltimore 1133 Boston 1133 Denver 1104 San Francisco 1098 San Diego 1076 Sacramento 1045 Los Angeles 1024 Chicago 1017 Philadelphia 1011 Minneapolis 1011 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 mean(X) 983.462 std deviation(S) 124.609 std error =S/(n)1/2 24.4378 t=(X-mean)/std error 3.4153 p value 0.0011