Question

City1	City 2	City 3	City 4
789	748	1831	1756
2051	1501	740	2125
765	1886	1554	1995
1645	1593	137	1526
1266	1474	2276	1746
2138	1913	2144	1616
1487	1218	1053	1958
1622	1006	1120	1675
1169	343	1838	1885
2215	1494	1735	2204
167	580	1326	2409
2557	1320	1790	1338
634	1784	32	2076
1326	1044	1455	2375
1790	890	1913	1125
32	1708	1218	1326
1455	1913	1006	1790
	1218	343	32
	1006	1494	1455
	343	580

(1) Using the above table, data set has information on the account balances of customers at a bank’s four locations. Using that data set and an ? of 0.05, test the null hypothesis that the mean account balances are equal in the four towns using a one-way ANOVA in Excel?. Please provide a picture of the excel spreadsheet with the ANOVA Test results.

(2) Do you reject the null hypothesis or not? Indicate on which part of the Excel output you base your decision.

(3) Assuming that an acquaintance of yours has never heard of ANOVA, explain to him what the decision in part (b), i.e., “rejecting H₀” or “not rejecting H₀” means in this context at a level that can be understood by a high school senior.

Answer 1

1) One-way ANOVA in excel

Null and Alternative Hypothesis:

2) At =0.05, and df1=3 and df2 =72, Critical Value of F_crit = 2.7318

And Test statistic F = 2.3527

As F < F_c, we fail to reject the null Hypothesis.

Also p-value =0.079 > =0.05, so we fail to reject the null Hypothesis.

3) Rejecting H0 means: Not all the mean account balance in four town are equal. As all mean account balance are not equal. So, we reject the null Hypothesis that they are equal in the four towns.

Not Rejecting H0 means: That we do not have enough evidence to claim that mean account balance in the four towns are not equal. So, we fail to reject that the mean account balance in the four towns is equal.