With many other options available, customers no longer let their money sit in a
ID: 3043029 • Letter: W
Question
With many other options available, customers no longer let their money sit in a checking account. For many years the mean checking balance has been $1,600. Do the sample data indicate that the mean account balance has declined from this value?
Recent years have also seen an increase in the use of ATM machines. When Mr. Selig took over the bank, the mean number of transactions per month per customer was 8; now he believes it has increased to more than 10. In fact, the advertising agency that prepares TV commercials for Century would like to use this on the new commercial being designed. Is there sufficient evidence to conclude that the mean number of transactions per customer is more than 10 per month? Could the advertising agency say the mean is more than 9 per month?
With many other options available, customers no longer let their money sit in a checking account. For many years the mean checking balance has been $1,600. Do the sample data indicate that the mean account balance has declined from this value?
Recent years have also seen an increase in the use of ATM machines. When Mr. Selig took over the bank, the mean number of transactions per month per customer was 8; now he believes it has increased to more than 10. In fact, the advertising agency that prepares TV commercials for Century would like to use this on the new commercial being designed. Is there sufficient evidence to conclude that the mean number of transactions per customer is more than 10 per month? Could the advertising agency say the mean is more than 9 per month?
Balance ATM Services Debit Interest City 1756 13 4 0 1 2 748 9 2 1 0 1 1501 10 1 0 0 1 1831 10 4 0 1 3 1622 14 6 0 1 4 1886 17 3 0 1 1 740 6 3 0 0 3 1593 10 8 1 0 1 1169 6 4 0 0 4 2125 18 6 0 0 2 1554 12 6 1 0 3 1474 12 7 1 0 1 1913 6 5 0 0 1 1218 10 3 1 0 1 1006 12 4 0 0 1 2215 20 3 1 0 4 137 7 2 0 0 3 167 5 4 0 0 4 343 7 2 0 0 1 2557 20 7 1 0 4 2276 15 4 1 0 3 1494 11 2 0 1 1 2144 17 3 0 0 3 1995 10 7 0 0 2 1053 8 4 1 0 3 1526 8 4 0 1 2 1120 8 6 1 0 3 1838 7 5 1 1 3 1746 11 2 0 0 2 1616 10 4 1 1 2 1958 6 2 1 0 2 634 2 7 1 0 4 580 4 1 0 0 1 1320 4 5 1 0 1 1675 6 7 1 0 2 789 8 4 0 0 4 1735 12 7 0 1 3 1784 11 5 0 0 1 1326 16 8 0 0 3 2051 14 4 1 0 4 1044 7 5 1 0 1 1885 10 6 1 1 2 1790 11 4 0 1 3 765 4 3 0 0 4 1645 6 9 0 1 4 32 2 0 0 0 3 1266 11 7 0 0 4 890 7 1 0 1 1 2204 14 5 0 0 2 2409 16 8 0 0 2 1338 14 4 1 0 2 2076 12 5 1 0 2 1708 13 3 1 0 1 2138 18 5 0 1 4 2375 12 4 0 0 2 1455 9 5 1 1 3 1487 8 4 1 0 4 1125 6 4 1 0 2 1989 12 3 0 1 2 2156 14 5 1 0 2Explanation / Answer
i ) X : Account Balance
Xbar = 1499.987
S.D(X) = 596.9049
n=60
We want to test the hypothesis that
The mean account balance less than $1600.
I.e . Ho : mu =1600 against H1 : mu < 1600.
Under Ho the test statistic is
z =( xbar-mu ) / ( S.D(X) /sqrt(n)) ~ N(0,1)
z = (1499.987 -1600 ) / ( 596.9049 / sqrt(60))
= -1.2994
Critical value :
alpha = level of significance =0.05
Z 0.05 = 1.64
Here abs(Z) < Z tabulated it is not significant at 5% level of significance. Hence we accept Ho at 5% l.o.s
Conclusion : There is no sufficient evidences to claim that mean account balance is $1600.
ii) Y : no .of times ATM ( no .of transactions) are used.
Ybar =10.3
S.D(Y) = 4.2954
n=60
We want to test the hypothesis that
The mean number of transaction is greater than 10
i.e Ho : mu =10 against H1 : mu > 10
Under Ho the test statistic is
z= (ybar -mu ) /(S.D. (Y) /sqrt(n)) ~ N(0,1)
z = (10.3 -10) / (4.2954/sqrt(60))
z = 0.5409
Critical value :
alpha = level of significance =0.05
Z 0.05 = 1.64
Here z < Z tabulated it is not significant at 5% level of significance. Hence we accept Ho at 5% l.o.s
Conclusion : There is no sufficient evidences to claim that the mean number of transaction is greater than 10.
suppose we want to test
The mean number of transaction is greater than 9
Ho : mu =9 against H1 : mu > 9
Under Ho the test statistic is
z= (ybar -mu ) /(S.D. (Y) /sqrt(n)) ~ N(0,1)
z = (10.3 -9) / (4.2954/sqrt(60))
z =2.3443
Critical value :
alpha = level of significance =0.05
Z 0.05 = 1.64
Here z > Z tabulated it is significant at 5% level of significance. Hence we reject Ho at 5% l.o.s
Conclusion : There is sufficient evidences to claim that the mean number of transaction is greater than 9.
Sr.No. Balance ATM Services Debit Interest City 1 1756 13 4 0 1 2 2 748 9 2 1 0 1 3 1501 10 1 0 0 1 4 1831 10 4 0 1 3 5 1622 14 6 0 1 4 6 1886 17 3 0 1 1 7 740 6 3 0 0 3 8 1593 10 8 1 0 1 9 1169 6 4 0 0 4 10 2125 18 6 0 0 2 11 1554 12 6 1 0 3 12 1474 12 7 1 0 1 13 1913 6 5 0 0 1 14 1218 10 3 1 0 1 15 1006 12 4 0 0 1 16 2215 20 3 1 0 4 17 137 7 2 0 0 3 18 167 5 4 0 0 4 19 343 7 2 0 0 1 20 2557 20 7 1 0 4 21 2276 15 4 1 0 3 22 1494 11 2 0 1 1 23 2144 17 3 0 0 3 24 1995 10 7 0 0 2 25 1053 8 4 1 0 3 26 1526 8 4 0 1 2 27 1120 8 6 1 0 3 28 1838 7 5 1 1 3 29 1746 11 2 0 0 2 30 1616 10 4 1 1 2 31 1958 6 2 1 0 2 32 634 2 7 1 0 4 33 580 4 1 0 0 1 34 1320 4 5 1 0 1 35 1675 6 7 1 0 2 36 789 8 4 0 0 4 37 1735 12 7 0 1 3 38 1784 11 5 0 0 1 39 1326 16 8 0 0 3 40 2051 14 4 1 0 4 41 1044 7 5 1 0 1 42 1885 10 6 1 1 2 43 1790 11 4 0 1 3 44 765 4 3 0 0 4 45 1645 6 9 0 1 4 46 32 2 0 0 0 3 47 1266 11 7 0 0 4 48 890 7 1 0 1 1 49 2204 14 5 0 0 2 50 2409 16 8 0 0 2 51 1338 14 4 1 0 2 52 2076 12 5 1 0 2 53 1708 13 3 1 0 1 54 2138 18 5 0 1 4 55 2375 12 4 0 0 2 56 1455 9 5 1 1 3 57 1487 8 4 1 0 4 58 1125 6 4 1 0 2 59 1989 12 3 0 1 2 60 2156 14 5 1 0 2 Sample mean 1499.867 10.3 4.416667 0.433333 0.266667 2.4 Std.dev 596.9049 4.295445 1.976915 0.499717 0.445948 1.107754Related Questions
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