Question

First National Bank and City National Bank are competing for customers who would like to open IRAs. Twenty two weeks are randomly selected and total number of deposits from IRAs is noted for each week. A summary of data from the survey is as follows:

First National Bank: X¯ = 4.1, s = 1.2

City National Bank: X¯ = 3.5, s = 0.9

Perform a testing procedure to find out any significant difference between the mean weekly deposits from IRAs for each bank. Use α = 0.02. Find the p value.

Answer 1

For Sample 1 :

x̅1 = 4.1, s1 = 1.2, n1 = 22

For Sample 2 :

x̅2 = 3.5, s2 = 0.9, n2 = 22

Null and Alternative hypothesis:

Ho : µ1 = µ2

H1 : µ1 ≠ µ2

Pooled variance :

S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2) = ((22-1)*1.2² + (22-1)*0.9²) / (22+22-2) = 1.1250

Test statistic:

t = (x̅1 - x̅2) / √(s²p(1/n1 + 1/n2 ) = (4.1 - 3.5) / √(1.125*(1/22 + 1/22)) = 1.8762

df = n1+n2-2 = 42

p-value = T.DIST.2T(ABS(1.8762), 42) = 0.0676

Decision:

p-value > α, Do not reject the null hypothesis