SOLUTION: A credit card watchdog group claims that there is a difference in the mean credit card debts of households in California and Illinois. The results of a random survey of 900 house

Question 1177875: A credit card watchdog group claims that there is a difference in the mean credit card debts of households in California and Illinois. The results of a random survey of 900 households from each state are shown below. The two samples are independent. Assume that σ1=$3545 for California and σ2=$2119 for Illinois. Do the results support the group's claim? Use α=0.01.

California = 13254
n= 900
Illinois = 16866
n=900

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is strictly speaking a two sample t-test, but the samples are so large a z-test will be sufficient
z=(difference in means)/ sqrt (sigma1^2/n1+ sigma2^2/n2)
=-3632/137.67
=-26
very highly significant, p-value=0
There is a difference between the two states, meaning that both values could not come from the same population.

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